Question

Evaluate the sum of each series as defined a=-4, r= 4, n=7

Answer 1

This is a geometric series question and we knkow this because we were given a common ratio (r) value.

The formula for calculating the sum of a GP, where r>1 is:

`S_n=(a(r^n-1))/(r-1)`

Where a=4, r=4, and n=7

Now, Substituting these given parameters into the formula above, we will have:

`\begin{gathered} S_7=(4(4^7-1))/(4-1) \\ =(4(16384-1))/(3) \\ =(4(16383))/(3) \\ =(65532)/(3) \\ =21844 \end{gathered}`

Final answer.

The sum of the first seven terms of this geometric series is 21844.