Question

What is the sum of the geometric sequence-1,6,36 if there are 6 terms

Answer 1

Answer:

The sum is $9,331$

Step-by-step explanation:

we have

$1,6,36,...$

we have

$a1=1$

$a2=6$

$a3=36$

Find the common ratio r

$a2/a1=6/1=6$

$a3/a2=36/6=6$

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

$S=a1\frac{(1-r^{n})}{(1-r)}$

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

$n=6$

$a1=1$

$r=6$

substitute

$S=(1)\frac{(1-(6)^{6})}{(1-6)}$

$S=\frac{(1-(6)^{6})}{(-5)}$

$S=9,331$