Question

The sum of first five terms of the series 2,8,32....is

Answer 1

2*4=8
8*4=32
32*4=128
128*4=512.
So, sum of the first five terms of the series is
2+8=10+32=42+128=170+512=682..
Do, the sum of the numbers in the sequence is 682.
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Answer 2

The sum of first five terms of the series 2,8,32....is 511.50.

Given:

The series 2,8,32....

To Find:

The sum of first five terms of the series 2,8,32....

Step-by-step explanation:

Formula Used:

Sum of  the  geometric sequence $=\frac{a(r^{n} -1)}{(r-1)}$   ------- formula no.01.

Where

a =  first number

r=  common ratio

n=  number of terms

Solution:

As given,The series 2,8,32....

This series in the  geometric sequence.

a=2

r$=\frac{8}{2} =4$

n=5

Applying the formula no.01.

The sum of first five terms  the geometric sequence $=\frac{2(4^{5} -1)}{(5-1)}$

                                                                                         $=\frac{2(1024-1)}{4}$

                                                                                          $=\frac{2\times 1023}{4}$

                                                                                           $=511.50$

Thus,the sum of first five terms of the series 2,8,32....is 511.50.

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