Progressions

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What is the nth term formula for the series 1.2.3 + 2.3.4 + 3.4.5 + …..?

n(n+1)+2(n+1)

n(n+1)(n+2) (correct)

n(n+1)(n+2)(n+3)

n(n+1)+2n

What is the common difference of the series 1.2.3 + 2.3.4 + 3.4.5 + …..?

4

1 (correct)

3

2

How many terms are being selected in the series 1.2.3 + 2.3.4 + 3.4.5 + ….. to find the sum?

n+2

n (correct)

n-1

n+1

What is the formula for the sum of an arithmetic series?

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

What is the property of an arithmetic sequence where the mean of the sequence is equal to the sum of the first and last terms divided by 2?

Mean is equal to the sum of the first and last terms divided by 2 Signup and view all the answers

What is the common difference of the arithmetic progression 2, 7, 12, 17, 22, …?

5 Signup and view all the answers

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

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

How can you determine if a sequence is an arithmetic progression?

By checking if the difference between each term is constant Signup and view all the answers

What is the pth term of an arithmetic progression?

a + (p - 1)d Signup and view all the answers

What is the representation of an arithmetic progression if 'a' is the first term and 'd' is the common difference?

a, a + d, a + 2d, a + 3d, … Signup and view all the answers

What is the general form of an arithmetico-geometric sequence?

a, (a + d)r, (a + 2d)r^2, ... Signup and view all the answers

What is the formula for the nth term of an arithmetico-geometric sequence?

[a + (n - 1)d]r^(n-1) Signup and view all the answers

What is the formula for the sum of n terms of an arithmetico-geometric sequence when r ≠ 1?

a(1 - r^n) + dr(1 - r^(n-1)) / (1 - r) Signup and view all the answers

What is the condition for the sum of an infinite arithmetico-geometric sequence to exist?

|r| < 1 Signup and view all the answers

What is the formula for the sum of an infinite arithmetico-geometric sequence when |r| < 1?

a / (1 - r) + dr / (1 - r)^2 Signup and view all the answers

What is a necessary condition for a sequence to be a progression?

The terms of the sequence follow a certain pattern Signup and view all the answers

What can be obtained by adding or subtracting the terms of a sequence?

A series Signup and view all the answers

What is the general term formula for the progression 1, 3, 5, 7, 9, ……..?

Tn = 2n - 1 Signup and view all the answers

What are the three main types of progressions?

Arithmetic, geometric, and harmonic Signup and view all the answers

What is a common characteristic of all progressions?

The terms follow a certain pattern Signup and view all the answers

In an arithmetic progression, what is the significance of the common difference?

It is the constant difference between any two consecutive terms. Signup and view all the answers

What is the condition for a sequence to be an arithmetic progression?

The difference between any two consecutive terms is constant. Signup and view all the answers

What is the general term of an arithmetic progression?

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

How can you determine if a sequence is not an arithmetic progression?

By checking if the difference between consecutive terms is not constant. Signup and view all the answers

What is the significance of the first term and common difference in an arithmetic progression?

They are used to find the general term of the progression. Signup and view all the answers

What is the general term of a geometric progression?

ar^(n-1) Signup and view all the answers

If a, b, c are in geometric progression, what is the relationship between them?

b^2 = ac Signup and view all the answers

What is the formula for the pth term from the end of a finite geometric progression?

ar^(n-p) Signup and view all the answers

What is the condition for a sequence to be a geometric progression?

The ratio of each term to its previous term is constant. Signup and view all the answers

What is the formula for the nth term of a geometric progression?