Question

For a GP if S3 = 16 , S6=144
find the first term and the common
ratio of the GP.
​

Answer 1

Given : S₃ = 16  and S₆ = 144

To Find :   the first term and the common ratio

Solution:

S₃ = 6  and S₆ = 144

Sₙ =  a(rⁿ - 1)/(r - 1)

a = first term

r = common ratio

n = number of terms

S₃ =  a(r³ - 1)/(r - 1)  = 16

S₆ =  a(r⁶ - 1)/(r - 1) = 144

S₆ / S₃ = 144/16  = 9

=> S₆ / S₃ =  {a(r⁶ - 1)/(r - 1)} /   {a(r³ - 1)/(r - 1)}

= (r⁶ - 1) / (r³ - 1)

= (r³+ 1)

r³+ 1 = 9

=> r³ = 8

=> r = 2

S₃ =  a(r³ - 1)/(r - 1)  = 16

=> a(2³ - 1)/(2 - 1)  = 16

=> a ( 7) = 16

=> a = 16/7

First term = 16/7

and common ratio =2

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