Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given geometric series
[tex]1+4+16+64+...[/tex]STEP 2: Write the formula to calculate the sum of nth terms of a geometric series
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]where r is the common ration
a is the first term
Sn is the sum of the nth term
n is the number of terms
STEP 3: Write the required data values
[tex]n=14,a=1,r=\frac{T_2}{T_1}=\frac{4}{1}=4[/tex]STEP 4: substitute the values to find the sum of the first 14 terms
[tex]\begin{gathered} S_{14}=\frac{1(4^{14}-1)}{4-1} \\ =\frac{268435456-1}{3}=\frac{268435455}{3}=89478485 \end{gathered}[/tex]Hence, the sum of the first 14 terms of the given geometric series is 89478485
