Question

The first term of a geometric sequence is 7, and the ratio (multiplier) is 3. what is the sum of the first 5 terms of the sequence? user: what is the 8th term of this geometric sequence? 6, 48, 384, 3072, . . .

Answer 1

Hello,

1)
$a_{1}=7$
$a_{2}=7*3$
$a_{3}=7*3^2$

$a_{n}=7*3^{n-1}$

$s=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}=7*(1+3^1+3^2+3^3+3^4)$
$=7*\frac{3^{5}-1}{3-1}$
$=7*242/2=847$

2)
$b_{8}=6*8^{8-1}=12582912$