Question

What is the sum of the geometric series 20 + 21 + 22 + 23 + 24 + … + 29?

a) 1,023
b)511
c)2,407
d)1,012

Answer 1

there are no answer is right !

Answer 2

The answer is a) 1,023

Explanation:

A geometric series is a series with a constant ratio between successive terms. So, the given series must be in the exponential form.

`2^(0)+2^(1)+2^(2)+2^(3)+2^(4)+2^(5)+2^(6)+2^(7)+2^(8)+2^(9)`

We have been asked about the sum of the geometric series :

`1+2+8+16+32+64+128+256+512`

Sum = 1023

Hence, option A is the answer.

If Solving the series as it is given:

The given series : 20+21+22+23+....+29 is an arithmetic series.

Its sum is :
`(10(20+29))/(2)=245`

I have solved the question both ways. Both the answers are right with respect to the series name.