First slide

Geometric progression

Question

The sum of an infinite number of terms of a G.P. is 20, and the sum of their squares is 100, then the first term of the G.P is

Moderate

A

$5$
B

$\frac{8}{5}$
C

$\frac{3}{5}$
D

8

Solution

$Given that \frac{a}{1 - r} = 20, \frac{a^{2}}{1 - r^{2}} = 100 \Rightarrow \frac{a}{1 + r} = 5 \Rightarrow a = 8$

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