Question

What is the sum of the geometric sequence 1,4,16 if there are 8 terms

Answer 1

Answer:

$\large\boxed{21845}$

Step-by-step explanation:

The formula of a sum of terms of a geometric sequence:

$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$

We have:

$a_1=1,\ a_2=4,\ a_3=16\ and\ n=8$

Calculate the common ratio:

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_{n+1}}{a_n}\\\\r=\dfrac{4}{1}=4\\\\r=\dfrac{16}{4}=4$

CORRECT :)

Substitue:

$S_8=1\cdot\dfrac{1-4^8}{1-4}=\dfrac{1-65536}{-3}=\dfrac{-65535}{-3}=21845$