Question

Given a G.P. with a=729 & 7th term 64, determine S7.

Answer 1

✪ Geometric Progression ✪

a = 729

7th term = 64

$a {r}^{7 - 1} = 64 \\ \\ = > 729 {r}^{6} = 64 \\ \\ = > {r}^{6} = ({ \frac{2}{3} })^{6} \\ \\ = > r = \frac{2}{3} \\ \\ \\ sn = a( \frac{1 - {r}^{n} }{1 - r} ) \\ \\ = > s7 = 729( \frac{1 - { (\frac{2}{3} )}^{7} }{1 - \frac{2}{3} } ) \\ \\ = > s7 = 729( \frac{1 - { (\frac{128}{2187} )} }{1 - \frac{2}{3} } ) \\ \\ = > s7 = 729( \frac{ \frac{2059}{2187} }{ \frac{1}{3} } ) \\ \\ = > s7 = 729 \times \frac{2059}{2187} \times 3 \\ \\ = > s7 = 2059$

So, your answer S7 = 2059.