find the 1st term of the geometric progression in which s8=510, r=2

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Solution

$Let a be the first term and r be the common ratio of the given geometric progression then, Sum of n terms of a GP is written as S_{n} = \frac{a (r^{n} - 1)}{(r - 1)} Putting r = 2 and n = 8, we get, S_{8} = \frac{a (2^{8} - 1)}{(2 - 1)} \Rightarrow 510 = \frac{a (256 - 1)}{1} [as S_{8} = 510] \Rightarrow 510 = a \times 255 \Rightarrow a = \frac{510}{255} = 2 Therefore, first term of given geometric progression is 2$

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