Question

Find the sum of the geometric series with a1 = 243, r = -2/3, And n = 5

Answer 1

Answer:

Sum of 5 terms of give geometric series is 165.

Solution:

Need to find the sum of geometric series.  

Given that  

First term of geometric series $a_{1}$ = 243

Common ratio of geometric series r = $\frac{-2}{3}$

Number of terms in series = n = 5

Sum of geometric series when r < 1 is given by following formula

$s=\frac{a_{1}\left(1-r^{n}\right)}{1-r}$$\frac{243\left(1-\left(-\frac{2}{3}\right)^{5})\right.}{1-\left(\frac{-2}{3}\right)}$

$\frac{243\left(1-\left(\frac{-32}{243}\right)\right)}{1+\frac{2}{3}}$

$\frac{\frac{243(243+32)}{243}}{\frac{5}{3}}$

= 55 x 3 = 165  

Hence sum of 5 terms of give geometric series is 165.