Gr12 Mathematics: Ch 1.6 Infinite Series

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

Tn = a × (n - 1) d

Tn = a / (n - 1) d

Tn = a - (n - 1) d

Tn = a + (n - 1) d (correct)

What is the sum of the first 100 positive integers?

4000

6000

7000

5050 (correct)

What is the general formula for a finite arithmetic series?

Sn = n / 2 × (a + l)

Sn = n × (a + l)

Sn = n / 2 × (2a + (n - 1) d) (correct)

Sn = n × (a - l)

What is the last term (l) in an arithmetic sequence?

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

What is the advantage of using Karl Friedrich Gauss's method?

It is a simple and efficient method for summing a finite arithmetic series Signup and view all the answers

What is the common difference (d) in an arithmetic sequence?

The constant difference between any term and the previous term Signup and view all the answers

What is the formula for Sn when the last term l is unknown?

Sn = n / 2 × (2a + (n - 1) d) Signup and view all the answers

What is the purpose of deriving the general formula for a finite arithmetic series?

To find the sum of any finite arithmetic series Signup and view all the answers

What is the formula for the sum of an arithmetic sequence from the first term (a) to the last term (l)?

$S_n = rac{n}{2} (a + l)$ Signup and view all the answers

How many terms are being added together in the sum: $S_{100} = 1 + 2 + 3 + … + 100$?

100 Signup and view all the answers

What is the value of $d$ in the sequence of positive integers?

1 Signup and view all the answers

What is the purpose of adding corresponding pairs of terms in Karl Friedrich Gauss's method?

To simplify the sum Signup and view all the answers

What is the value of $S_{100}$ when using Karl Friedrich Gauss's method?

5050 Signup and view all the answers

What is the formula for the $n$-th term of an arithmetic sequence?

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

What is the formula for $S_n$ when the last term $l$ is unknown?

$S_n = rac{n}{2} (2a + (n - 1) d)$ Signup and view all the answers

What is the advantage of using formulas to calculate the sum of an arithmetic sequence?

It is faster than listing out all the terms Signup and view all the answers

What is the sum of the first 50 positive integers?

1275 Signup and view all the answers

If the sum of the first 20 terms of an arithmetic sequence is 210, what is the common difference?

2 Signup and view all the answers

What is the sum of the first 15 terms of an arithmetic sequence with a first term of 3 and a common difference of 2?

135 Signup and view all the answers

If the sum of the first 25 terms of an arithmetic sequence is 625, what is the first term?

10 Signup and view all the answers

What is the sum of the first 30 terms of an arithmetic sequence with a last term of 60 and a common difference of 2?

930 Signup and view all the answers

If the sum of the first 18 terms of an arithmetic sequence is 342, what is the last term?

38 Signup and view all the answers

What is the sum of the first 12 terms of an arithmetic sequence with a first term of 2 and a last term of 26?

156 Signup and view all the answers

If the sum of the first 40 terms of an arithmetic sequence is 1040, what is the common difference?

4 Signup and view all the answers