Question

The first three terms of a geometric series are 4p, (3p+15) and (5p+20) respectively, where p is a positive constant. (i) Show that 11p 2 − 10p − 225 = 0

Answer 1

SOLUTION

GIVEN

The first three terms of a geometric series are 4p, (3p+15) and (5p+20) respectively, where p is a positive constant.

TO PROVE

11p² − 10p − 225 = 0

CONCEPT TO BE IMPLEMENTED

If three terms a , b , c are in Geometric Progression then

$\sf{ {b}^{2} = ac}$

EVALUATION

Here it is given that the first three terms of a geometric series are 4p, (3p+15) and (5p+20) respectively, where p is a positive constant.

So by the given condition

$\sf{ {(3p + 15)}^{2} = 4p(5p + 20)}$

$\sf{ \implies \: 9 {p}^{2} + 90p + 225 = 20 {p}^{2} + 80p}$

$\sf{ \implies \: 9 {p}^{2} + 90p + 225 - 20 {p}^{2} - 80p = 0}$

$\sf{ \implies \: - 11 {p}^{2} + 10p + 225 = 0}$

$\sf{ \implies \: 11 {p}^{2} - 10p - 225 = 0}$

Hence proved

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