# Arithmetic and Geometric Progressions

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What is the formula for infinite terms of a GP?

## Sum of infinite terms

Sum of infinite terms of a GP is 12. If the first term is 8, what is the 4th term of this GP?
1. $\frac{8}{27}$

2. $\frac{4}{27}$

3. $\frac{8}{20}$

4. $\frac{1}{3}$

Choice A. $\frac{8}{27}$

## Detailed Solution

Given : $S_{\infty} = 12 and a = 8$

$S_{\infty} = \frac{a}{1 - r}$
$12 = \frac{8}{1 - r}$
$l - r = \frac{2}{3}$
$r = \frac{1}{3}$

Now $t_{4} = 8 * \frac{1}{3}^{3}$
$t_{4} = \frac{8}{27}$

Correct Answer: $\frac{8}{27}$

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## More questions from Progressions

With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.