Question

the first team of a GP is -20 and the 10th term is 10240. find S11 of this GP

Answer 1

Given that the first term of a GP is -20 and the 10th term is 10240.

We need to find S11 of this GP.

The first term is a = -20 and the tenth term is ar^9 = 10240. So,

$\begin{gathered} \frac{ar^9}{a}=\frac{10240}{-20} \\ r^9=-512 \\ r=(-512)^{\frac{1}{9}} \\ r=-2 \end{gathered}$

We know that the sum of n terms of gp is given by:

$S_n=\frac{a(1-r^n)}{(1-r)}$

The sum of 11 terms of the gp is:

$\begin{gathered} S_{11}=\frac{-20(1-(-2)^{11}^{})}{1-(-2)} \\ =\frac{-20(1-(-2048))}{1+2} \\ =\frac{-20(2049)}{3} \\ =-20(683) \\ =-13660 \end{gathered}$

Thus, the value of S11 is -13660.