Question

the first term of gp is 27 and iths 8th term is1÷81. fimd the sum of first seven terms of gp

Answer 1

The answer is given below :

First term of the GP = 27

Let, r be the common ratio.

8th term = 1/81

$= > first \: term \: \times {r}^{8 - 1}= \frac{1}{81} \\ \\ = > 27 \times {r}^{7} = \frac{1}{81} \\ \\ = > {r}^{7} = \frac{1}{ {3}^{7} } \\ \\ = > r = \frac{1}{3}$

So, common ratio, r = 1/3

Now, the sum of the first seven terms

$= \frac{first \: term \times (1 - {r}^{7} )}{1 - r} \\ \\ = \frac{27 \times (1 - \frac{1}{2187} )}{1 - \frac{1}{3} } \\ \\ = \frac{1093}{27}$

Thank you for your question.