FAQs on Sum to Infinite (G.P.): Algebra, Quantitative Reasoning

Question 1

1. What is a geometric progression (G.P.)?

Accepted Answer

Ans. A geometric progression (G.P.) is a sequence of numbers in which each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Question 2

2. How do you find the sum to infinity of a geometric progression?

Accepted Answer

Ans. To find the sum to infinity (S∞) of a geometric progression (G.P.), you need to determine whether the common ratio (r) is between -1 and 1. If it is, you can use the formula S∞ = a / (1 - r), where 'a' is the first term of the G.P.

Question 3

3. What happens if the common ratio of a geometric progression is greater than 1?

Accepted Answer

Ans. If the common ratio (r) of a geometric progression (G.P.) is greater than 1, the G.P. will diverge to infinity. This means there is no finite sum to infinity for such G.P.

Question 4

4. Can the sum to infinity of a geometric progression be negative?

Accepted Answer

Ans. No, the sum to infinity (S∞) of a geometric progression (G.P.) cannot be negative. The sum will either be a positive finite value, zero (if the common ratio is 1), or it will diverge to infinity (if the common ratio is greater than 1).

Question 5

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

Accepted Answer

Ans. The formula for finding the nth term of a geometric progression (G.P.) is given by the formula an = a * r^(n-1), where 'an' represents the nth term, 'a' is the first term, 'r' is the common ratio, and 'n' is the position of the term in the sequence.

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