Question

In a gp a=729 and 7th term is 64 find the sum of 7 terms

Answer 1

HEY MATE !!!

a=729

a7=64

We know that n th term of a G.P. =

${ar}^{n - 1}$

${a}^{7} = {ar}^{6}$

putting the values,

$64 = 729 {r}^{6} \\ \ {r}^{6} = \frac{64}{729} \\ {r}^{6} = ( { \frac{2}{3} )}^{6} \\ comparing \: the \: powers\\ r = \frac{2}{3}$

We need to find the sum of first 7terms.

$sn = \frac{a(1 - {r}^{n} )}{1 - r} \\ \\ s7= \frac{a(1 - {r}^{8} )}{1 - r} \\ \\ = \frac{729(1 - {( \frac{2}{3}) }^{7} ) }{1 - \frac{2}{3} } \\ \\ = \frac{729( 1 - \frac{128}{2187} )}{ \frac{3 - 2}{3} } \\ \\ = 729 \times \frac{2059}{2187} \times 3 \\ \\ = 2187 \times \frac{2059}{2187} \\ \\ = 2059$

Thus the sum of first 7 terms is 2059

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