Question

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

Answer 1

SOLUTION

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:

$S_n=\frac{a(r^n-1)}{r-1}$

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

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

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

Final answer.

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