Find the first term of a GP

Algebra Level 1

x , 3.75 , 5.625 \large{\mathsf{x,3.75,5.625}}

The numbers shown above form a geometric progression. Find x \mathsf{x} .


The answer is 2.5.

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1 solution

A geometric sequence follows the pattern:

a , a r , a r 2 , . . . a, ar, ar^2, ... where a a is the first term and r r is the common ratio. Hence, in this case, we are asked to find the value of a a , knowing that:

a = x a = x

a r = 3.75 ar= 3.75

a r 2 = 5.625 ar^2 = 5.625

If we divide 5.625 by 3.75 we get the common ratio. = 3 2 \frac{3}{2}

Then we divide 3.75 by the common ratio to get a a . = 2.5

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