Question

Find out four such posts in the ratio range that the third post is 9 plus for the first term and the second post is 10 more than the 4th position.

Answer 1

Solution -

According to the question we know that

T3 = T1 +9

so, ar² = a+9

ar²-a = 9_________(1)

T2 = T4 + 18

ar = ar³+18

ar-ar³ = 18__________(2)


If we divide both equations

$\frac{ar {}^{2} - ar {}^{3} }{ar {}^{2} - a} = \frac{182}{9}$


$\frac{ar(1 - r {}^{2}) }{ - a(1 - r {}^{2} )} = \frac{1}{2}$

r = -2


if we put the value of r in the first equation then,

a(-2)²-a = 9

3a = 9

a = 3

so,

T1 = 3
T2 = 3×(-2) => -6
T3 = 3×(-2)² => 12
T4 = 3×(-2)3 => -24


I hope it's help you

Regards : Sangela