Question

Evaluate each geometric series described A1=4, r=4, n=9

Answer 1

Given:

`\begin{gathered} A_1=4 \\ r=4 \\ n=9 \end{gathered}`

To Determine: The geometric series

Solution

The formula for evaluating the nth term of a geometric series is given as

`\begin{gathered} S_n=(a(r^n-1))/(r-1),where,r>1 \\ OR \\ S_n=(a(1-r^n))/(1-r) \end{gathered}`

Substitute the given into the formula

`\begin{gathered} r>1 \\ S_n=(a(r^n-1))/(r-1) \\ a=A_1=4 \\ r=4 \\ n=9 \\ S_9=(4(4^9-1))/(4-1) \\ S_9=(4(262144-1))/(3) \\ S_9=(4(262143))/(3) \\ S_9=(1048572)/(3) \\ S_9=349524 \end{gathered}`

Hence, the geometric series is 349524