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

Find the sum of the geometric series with a1 = 243,

sebastianapolo5

07.01.2022

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.

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anitadefrances

07.05.2021

x=1/2

Step-by-step explanation:

4/5x-1/10=3/10

4/5x=2/5

x= 1/2.

Hope this helps :D

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