Question

Find the sum of the first 4 terms of the series.

2-8+32-128+.....
a.
–101
b.
–103
c.
–102
d.
–104


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

Answer: Option c. (-102) is the sum of first four terms of the sequence.

Explanation:

In the sequence 2-8+32-128..... we know number of terms n=4

First term A(1)=2

Ratio of the terms r = (-4)

And we have to calculate the sum of four terms

We know the formula for this question is

`\sum_(K=0)^(n-1)A(1)r^(k)=A(1)((1-r^(n))/(1-r))`

`\sum_(K=0)^(4-1)A(1)r^(k)=A(1)((1-(-4)^(4))/(1-(-4)))`

`Sum=2((1-(4)^(4))/(1+4))`
`= 2((1-266)/(5))   = 2((-255)/(5))   =2(-51)`

Sum of first 4 terms is (-102)