Question

If the product of four consecutive terms in gp is 625 find the first term

Answer 1

Step-by-step explanation:

Let a, ar, ar², ar³ be the four consecutive terms of GP.

Since, the product of these four terms is 625.

So, a* ar* ar²* ar³ = 625

Since, the product of the four terms is 625. So, the common ratio r = 1

Therefore, a* ar* ar²* ar³ = 625

a* a* a* a = 625

a⁴ = 625

a⁴ = 5⁴

So, a = 5

Therefore, the first term of the given GP is 5.

Answer 2

Concept

A GP or a geometric progression is a series of numbers in which the common ratio between any two consecutive terms is constant.

Given

the product of four consecutive terms in a GP is 625

Find

we need to find the first term of the GP

Solution

Let us assume that the first term of the given GP is a and the common ratio is r

Then the GP will be

a/r, a, ar, ar^2

the product of these 4 terms is 625

a x ar x ar^2 x ar^3 = 625

a^4 x r^6 = 625

if r = 1

then, a^4 = 625

thus, a = 5

Therefore, the first term of the GP is 5.

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