Question

which term of GP 5,25, 125, 625.... is 5^10​

Answer 1

Concept:

A geometric progression, also termed a geometric sequence, is a non-zero numerical sequence in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value called the common ratio.

Given:

GP 5, 25, 125, 625

To find:

Term 5^10​ of the given GP.

Solution:

A geometric progression, also termed a geometric sequence, is a non-zero numerical sequence in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value called the common ratio.

A GP is given to us in this question, 5, 25, 125, 625

We have to find the 5^10 term of this question.

We know that:

First-term, a=5

The second term, ar=25 (5×5)

Common ratio, r=5

Now, let the nth term be =

$5^{10} =5*5^{9}$

$5*5^{9} =ar^{n-1} \\5*5^{9} =5*5^{n-1} \\5^{9} =5^{n-1} \\n=10$

Therefore 10th term of the GP is 5^10

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