Question

What is the sum of an 8 term geometric series if the first term is -11 and the last term is 859,375 and the common ratio is -5

Answer 1

Answer:716,144

Explanation:

Given

No of the terms in GP
`n=8`

First-term
`a=-11`

last term
`a_n=859,375\quad (ar^(n-1))`

Common ratio
`r=-5`

The Sum of a GP is given by

`S_n=(a(1-r^n))/(1-r)\quad \quad [r<1]`

Put the values

`\Rightarrow S_n=(-11(1-(-5)^8))/(1-(-5))\\\\\Rightarrow S_n=(-11* -390624)/(6)\\\\\Rightarrow S_n=(42,96,864)/(6)=716,144`