Question

How many termes of GP 2,22

,23

,24…….. are needed to give sum 2046
please give answer
its urgent
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Answer 1

Answer:

.of terms in a geometric series, i.e., x+x2+x3+⋯+xn is

∑nk=1xk=x(xn−1)x−1

In the case where x=2 we end up getting

2+4+...+2n=2(2n−1)2−1=2(2n−1)

We now want to find the n which sets this sum equal to 1022. We can figure this out by first using some arithmetic to simplify things:2(2n−1)=1022

2n−1=511

2n=512

We now take the base 2 of both sides.

log2(2n)=log2(512)

n=9

So, the answer to your original question of how many consecutive terms are needed for the geometric series 2+4+8+... to sum to 1022 is 9.