An algebra problem by Rahil Sehgal

Algebra Level 1

The sum of an infinite GP is 80/9 and

It's common ratio is -4/5.

Find its first term.


The answer is 16.

Rahil Sehgal by Rahil Sehgal , 20, India

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2 solutions

Rahil Sehgal
Mar 18, 2017

2 Helpful 0 Interesting 0 Brilliant 0 Confused

use the formula

s ∞ = a 1 1 − r s_{\infty}=\dfrac{a_1}{1-r}

Substitute:

80 9 = a 1 1 − ( − 4 5 ) \dfrac{80}{9}=\dfrac{a_1}{1-\left(\dfrac{-4}{5}\right)}

a 1 = 16 \boxed{a_1=16}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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