Question

What is the sum of the first 5 numbers in the series 1+2+4+8+16+32+...?16313263

Answer 1

Given data:

The series is 1 + 2 + 4 + 8 + 16 + 32 + ....

The given series is G.P because the common ratio for GP is,

`C\mathrm{}R\text{ = }(a_2)/(a_1)`

Here, the common ratio is 2.

Sum of the first five numbers ,

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

Here, a is first term that is 1

r is common ratio that is 2

n is the number

Therefore, sum is given as

`S_5=(1(2^5-1))/(2-1)`
`\begin{gathered} S_5=(32-1)/(1) \\ \text{ = 31} \end{gathered}`

Thus, the sum of first five terms is 31

The correct option is (2).