CH 1: Arithmetic sequences

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What is the common difference in the sequence -1, -4, -7, -10, -13, -16,...?

-1

5

-3 (correct)

2

What is the general formula for the nth term of an arithmetic sequence?

$T_n = a + (n-1)d$ (correct)

$T_n = a * n + d$

$T_n = a - d^n$

$T_n = a^2 + nd$

Which sequence is an arithmetic sequence?

-5, -3, -1, 1, 3,... (correct)

-2, 4, -8, 16, -32,...

1, 3, 6, 10, 15,...

-6, -12, -24, -48,...

What are the next three terms in the sequence 2, 6, 10, 14, 18, 22,...?

26, 30, 34 Signup and view all the answers

In an arithmetic sequence, what happens if the common difference is negative?

The terms become smaller in absolute value. Signup and view all the answers

What is the common difference in the sequence -5, -3, -1, 1, 3,...?

-2 Signup and view all the answers

Which term comes after 100 in the arithmetic sequence 3, 8, 13, 18,...?

$104$ Signup and view all the answers

What happens if the common difference in an arithmetic sequence is zero?

All terms are equal. Signup and view all the answers

$t_{10}$ in an arithmetic sequence is 25 with a common difference of 3. What is $t_1$?

$-7$ Signup and view all the answers

What is the common difference in the sequence: 2; 6; 10; 14; 18; 22;...?

4 Signup and view all the answers

In the sequence -1; -4; -7; -10; -13; -16;..., what are the next three terms?

-19, -22, -25 Signup and view all the answers

What is the common difference in the sequence: -5; -3; -1; 1; 3;...?

2 Signup and view all the answers

In the sequence: -1; 10; 21; 32; 43; 54;..., what is the next term after 54?

65 Signup and view all the answers

What is the common difference in the sequence: a - 3b; a - b; a + b; a + 3b;...?

2b Signup and view all the answers

What is the next term in the sequence: -2; -1.5; -1; -0.5; 0; 0.5; 1;...?

-0.75 Signup and view all the answers

In which sequence does the common difference equal 11?

-1; 10; 21; 32; 43; 54;... Signup and view all the answers

What is the result of adding the first and second terms in the sequence: 2; 6; 10; 14; 18; 22;...?

8 Signup and view all the answers

Which sequence demonstrates a decreasing pattern with a constant difference of -3?

-1; -4; -7; -10; -13; -16; Signup and view all the answers

Which pair of terms has a constant difference of $2b$ in the sequence: $a-3b;a-b;a+b;a+3b;$?

$a-b$ and $a+b$ Signup and view all the answers

What is the common difference in the sequence: -2, 2, 6, 10, 14,...?

4 Signup and view all the answers

For the sequence 7, 14, 21, 28,..., what is the first term?

-2 Signup and view all the answers

In the sequence: 3, 0, -3, -6,..., what is the common difference?

-3 Signup and view all the answers

What would be the next three terms in the sequence: 12, 9, 6, 3,...?

-3, -6, -9 Signup and view all the answers

Given the sequence -4, 0, 4, 8,..., what is the position of the term '20'?

$t_8$ Signup and view all the answers

Which of the following sequences is NOT an arithmetic sequence?

$2^2, 4^2, 6^2, 8^2,...$ Signup and view all the answers

For an arithmetic sequence with $t_1 = -8$ and $t_{10} = 22$, what is the common difference?

$\frac{15}{9}$ Signup and view all the answers

If the first term in an arithmetic sequence is 12 and the common difference is -5, what is the fifth term?

-8 Signup and view all the answers

What will be the next term in the sequence: $3x-5; x-2; x+1; 2x+4;...$?

$2x+6$ Signup and view all the answers

In the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ..., what is the common difference $d$?

$2b$ Signup and view all the answers

What is the next term in the sequence: $-2$, $-1.5$, $-1$, $-0.5$, $0$, $0.5$, $1$, ...?

$2.5$ Signup and view all the answers

If the first term of an arithmetic sequence is $5$ and the common difference is $3$, what is the $10^{th}$ term?

$31$ Signup and view all the answers

Which of the following sequences has a decreasing pattern with a common difference of $-3$?

$-1$, $-4$, $-7$, $-10$, $-13$, $-16$, ... Signup and view all the answers

What is the sum of the first two terms in the sequence: $2$, $6$, $10$, $14$, $18$, $22$, ...?

$8$ Signup and view all the answers

In which of the following sequences is the common difference equal to $11$?

$-1$, $10$, $21$, $32$, $43$, $54$, ... Signup and view all the answers

If the $10^{th}$ term of an arithmetic sequence is $25$ and the common difference is $3$, what is the first term?

$-4$ Signup and view all the answers

If the common difference in an arithmetic sequence is zero, what can be said about the sequence?

The sequence is constant, with all terms being equal. Signup and view all the answers

What is the general formula for the $n^{th}$ term of an arithmetic sequence with first term $a$ and common difference $d$?

$a_n = a + (n-1)d$ Signup and view all the answers

Which pair of terms in the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ... has a constant difference of $2b$?

$a - b$ and $a + b$ Signup and view all the answers

What is the common difference in the sequence $-5$, $-3$, $-1$, $1$, $3$,...?

$2$ Signup and view all the answers

If the first term of an arithmetic sequence is $5$ and the common difference is $3$, what is the $10^{th}$ term?

$41$ Signup and view all the answers

What is the general formula for the $n^{th}$ term of an arithmetic sequence with first term $a$ and common difference $d$?

$T_n = a + (n-1)d$ Signup and view all the answers

If the $10^{th}$ term of an arithmetic sequence is $25$ and the common difference is $3$, what is the first term?

$4$ Signup and view all the answers

What happens if the common difference in an arithmetic sequence is zero?

The sequence becomes a constant sequence Signup and view all the answers

In the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ..., what is the common difference $d$?

$2b$ Signup and view all the answers

Which pair of terms in the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ... has a constant difference of $2b$?

$a - b$ and $a + 3b$ Signup and view all the answers

What is the sum of the first two terms in the sequence: $2$, $6$, $10$, $14$, $18$, $22$, ...?

$8$ Signup and view all the answers

In the sequence: $-1$; $10$; $21$; $32$; $43$; $54$;..., what is the next term after $54$?

$65$ Signup and view all the answers

What is the next term in the sequence: $a - 3b$, $a - b$, $a + b$, $a + 3b$, ...?

$a + 5b$ Signup and view all the answers

If the first term of an arithmetic sequence is $-12$ and the common difference is $5$, what is the $10^{th}$ term?

$27$ Signup and view all the answers

In the sequence $-5$, $-3$, $-1$, $1$, $3$, ..., what is the sum of the first $5$ terms?

$0$ Signup and view all the answers

If the $6^{th}$ term of an arithmetic sequence is $18$ and the common difference is $4$, what is the first term?

$2$ Signup and view all the answers

Which of the following sequences is not an arithmetic sequence?

$1$, $4$, $9$, $16$, $25$, ... Signup and view all the answers

If the $10^{th}$ term of an arithmetic sequence is $35$ and the common difference is $-3$, what is the first term?

$11$ Signup and view all the answers

In the sequence $-2$, $-1.5$, $-1$, $-0.5$, $0$, $0.5$, $1$, ..., what is the sum of the first $7$ terms?

$0$ Signup and view all the answers

If the $5^{th}$ term of an arithmetic sequence is $20$ and the common difference is $6$, what is the $10^{th}$ term?

$50$ Signup and view all the answers

If the sum of the first $5$ terms of an arithmetic sequence is $30$ and the common difference is $4$, what is the first term?

$6$ Signup and view all the answers

Which of the following sequences has a decreasing pattern with a common difference of $-3$?

$-1$, $-4$, $-7$, $-10$, $-13$, ... Signup and view all the answers

CH 1: Arithmetic sequences

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Questions and Answers

What is the common difference in the sequence -1, -4, -7, -10, -13, -16,...?

What is the general formula for the nth term of an arithmetic sequence?

Which sequence is an arithmetic sequence?

What are the next three terms in the sequence 2, 6, 10, 14, 18, 22,...?

In an arithmetic sequence, what happens if the common difference is negative?

What is the common difference in the sequence -5, -3, -1, 1, 3,...?

Which term comes after 100 in the arithmetic sequence 3, 8, 13, 18,...?

What happens if the common difference in an arithmetic sequence is zero?

$t_{10}$ in an arithmetic sequence is 25 with a common difference of 3. What is $t_1$?

What is the common difference in the sequence: 2; 6; 10; 14; 18; 22;...?

In the sequence -1; -4; -7; -10; -13; -16;..., what are the next three terms?

What is the common difference in the sequence: -5; -3; -1; 1; 3;...?

In the sequence: -1; 10; 21; 32; 43; 54;..., what is the next term after 54?

What is the common difference in the sequence: a - 3b; a - b; a + b; a + 3b;...?

What is the next term in the sequence: -2; -1.5; -1; -0.5; 0; 0.5; 1;...?

In which sequence does the common difference equal 11?

What is the result of adding the first and second terms in the sequence: 2; 6; 10; 14; 18; 22;...?

Which sequence demonstrates a decreasing pattern with a constant difference of -3?

Which pair of terms has a constant difference of $2b$ in the sequence: $a-3b;a-b;a+b;a+3b;$?

What is the common difference in the sequence: -2, 2, 6, 10, 14,...?

For the sequence 7, 14, 21, 28,..., what is the first term?

In the sequence: 3, 0, -3, -6,..., what is the common difference?

What would be the next three terms in the sequence: 12, 9, 6, 3,...?

Given the sequence -4, 0, 4, 8,..., what is the position of the term '20'?

Which of the following sequences is NOT an arithmetic sequence?

For an arithmetic sequence with $t_1 = -8$ and $t_{10} = 22$, what is the common difference?

If the first term in an arithmetic sequence is 12 and the common difference is -5, what is the fifth term?

What will be the next term in the sequence: $3x-5; x-2; x+1; 2x+4;...$?

In the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ..., what is the common difference $d$?

What is the next term in the sequence: $-2$, $-1.5$, $-1$, $-0.5$, $0$, $0.5$, $1$, ...?

If the first term of an arithmetic sequence is $5$ and the common difference is $3$, what is the $10^{th}$ term?

Which of the following sequences has a decreasing pattern with a common difference of $-3$?

What is the sum of the first two terms in the sequence: $2$, $6$, $10$, $14$, $18$, $22$, ...?

In which of the following sequences is the common difference equal to $11$?

If the $10^{th}$ term of an arithmetic sequence is $25$ and the common difference is $3$, what is the first term?

If the common difference in an arithmetic sequence is zero, what can be said about the sequence?

What is the general formula for the $n^{th}$ term of an arithmetic sequence with first term $a$ and common difference $d$?

Which pair of terms in the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ... has a constant difference of $2b$?

What is the common difference in the sequence $-5$, $-3$, $-1$, $1$, $3$,...?

If the first term of an arithmetic sequence is $5$ and the common difference is $3$, what is the $10^{th}$ term?

What is the general formula for the $n^{th}$ term of an arithmetic sequence with first term $a$ and common difference $d$?

If the $10^{th}$ term of an arithmetic sequence is $25$ and the common difference is $3$, what is the first term?

What happens if the common difference in an arithmetic sequence is zero?

In the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ..., what is the common difference $d$?

Which pair of terms in the sequence $a - 3b$, $a - b$, $a + b$, $a + 3b$, ... has a constant difference of $2b$?

What is the sum of the first two terms in the sequence: $2$, $6$, $10$, $14$, $18$, $22$, ...?

In the sequence: $-1$; $10$; $21$; $32$; $43$; $54$;..., what is the next term after $54$?

What is the next term in the sequence: $a - 3b$, $a - b$, $a + b$, $a + 3b$, ...?

If the first term of an arithmetic sequence is $-12$ and the common difference is $5$, what is the $10^{th}$ term?

In the sequence $-5$, $-3$, $-1$, $1$, $3$, ..., what is the sum of the first $5$ terms?

If the $6^{th}$ term of an arithmetic sequence is $18$ and the common difference is $4$, what is the first term?

Which of the following sequences is not an arithmetic sequence?

If the $10^{th}$ term of an arithmetic sequence is $35$ and the common difference is $-3$, what is the first term?

In the sequence $-2$, $-1.5$, $-1$, $-0.5$, $0$, $0.5$, $1$, ..., what is the sum of the first $7$ terms?

If the $5^{th}$ term of an arithmetic sequence is $20$ and the common difference is $6$, what is the $10^{th}$ term?

If the sum of the first $5$ terms of an arithmetic sequence is $30$ and the common difference is $4$, what is the first term?

Which of the following sequences has a decreasing pattern with a common difference of $-3$?

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