Answer:
Option (3)
Step-by-step explanation:
Given expression represents the sum of k terms of a geometric sequence.
[tex]\sum_{k=1}^{9}2(4)^{k-1}[/tex]
Since, formula to calculate the sum of a geometric sequence is given by,
[tex]\sum_{n=1}^{n}a(r)^{n-1}=\frac{a(1-r^n)}{1-r}[/tex]
By this formula,sum of 9 terms of the given sequence will be,
[tex]\sum_{k=1}^{9}2(4)^{k-1}=\frac{2(1-4^9)}{1-4}[/tex]
Therefore, Option (3) will be the answer.
