## If the sum of three consecutive terms in G.P. is 216 and sum of their products in pairs is 156, find them.

Question

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

## Answers ( )

Answer:pls mark as brianliest

Step-by-step explanation:Product of three terms = 216

(a/r) ⋅ a ⋅ a r = 216

a3 = 63

a = 6

Sum of their product in pairs = 156

(a/r) ⋅ a + a ⋅ ar + ar ⋅ (a/r) = 156

a2 / r + a2 r + a2 = 156

a2 [ (1/r) + r + 1 ] = 156

a² [ (1+r²+r)/r] = 156

a² (r²+r+1)/r = 156

(6²/r)(r²+r+1) = 156

(r²+r+1)/r = 156/36

(r²+r+1)/r = 13/3

3(r²+r+1) = 13 r

3r² + 3r + 3 – 13r = 0

3r² – 10r + 3 = 0

(3r – 1)(r – 3) = 0

3r – 1 = 0

3r = 1

r = 1/3

r – 3 = 0

r = 3

If a = 6, then r = 1/3

a/r = 6/(1/3) ==> 18

a = 6

ar = 6(1/3) ==> 2

If a = 6, then r = 1/3

a/r = 6/3 ==> 2

a = 6

ar = 6(3) ==> 18

Hence the required three terms are 18, 6 and 2 or 2, 6, 18.