Given data:
The series is 1 + 2 + 4 + 8 + 16 + 32 + ....
The given series is G.P because the common ratio for GP is,
[tex]C\mathrm{}R\text{ = }\frac{a_2}{a_1}[/tex]Here, the common ratio is 2.
Sum of the first five numbers ,
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Here, a is first term that is 1
r is common ratio that is 2
n is the number
Therefore, sum is given as
[tex]S_5=\frac{1(2^5-1)}{2-1}[/tex][tex]\begin{gathered} S_5=\frac{32-1}{1} \\ \text{ = 31} \end{gathered}[/tex]Thus, the sum of first five terms is 31
The correct option is (2).
