Question

Find the G.P. whose 2nd and 5th terms are `-3/2 "and" 81/16` respectively.

Answer 1

`T_2 = ar^(2 - 1)`

ar = `-3/2`   ...(1)

`T_5 = ar^(5 - 1)`

ar⁴ = `81/16`   ...(2)

Divide Equation 2 by Equation 1 to eliminate a:

`(ar^4)/(ar) = (81/16)/(-3/2)`

`r^3 = 81/16 xx (-2/3)`

`r^3 = -27/8`

Taking the cube root of both sides:

r = `root3(-27/8)`

r = `-3/2`

Substitute the value of r = `-3/2` back into Equation 1:

`a xx (-3/2)`

= `-3/2`

a = 1

T₁ ⇒ a = 1

 T₂ ⇒ ar = `1 xx (-3/2)`

= `-3/2`

 T₃ ⇒ `ar^2 = 1 xx (-3/2)^2`

= `9/4`

 T₄ ⇒ `ar^3 = 1 xx (-3/2)^3`

= `-27/8`