Question

The second term of a geometric progression is 24 and the third term is 12(x+1).
Find, in terms of x, the first term of the progression.​

Answer 1

Answer:

Term 1 of the progression will be , 48(x+1).

Step-by-step explanation:

Given , T2 = 24.

T3 = 12(x+1)

SOLUTION - The terms in gp works in the following format.

a , ar , ar^2.

So, second term of gp is 24.

so, T2 = 24

=> ar = 24 --------( 1)

Now T3 = 12(x+1)

ar^2 = 12( x+1) -------(2)

Now dividing equation 2 by equation 1.

ar^2 / ar = 12 (x+1) / 24.

r = (x+1)/ 2.

now put the value of r in equation 1.

ar = 24.

=> a (x+1) / 2 = 24

=> a = 48/ (x+1).

So, a= Term 1

Term1 = 48/(x+1).

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