Question

The sum of first two terms of a GP is 2 and the sum of the four terms
is 20. Determine the GP​

Answer 1

Answer:

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Step-by-step explanation:

We know common ratio in G.P. is equation

So, Let first term of G.P.  =  a

And Common ratio  =  r

So,  First four term in G.P.  ,  a  ,  ar , ar^2  and ar^3

So,  From first condition " The sum of the first two terms of a. GP is 2 . " we get

a  +  ar  = 2

a (  1  + r  ) = 2                                    ------- (1 )

And  From first condition " The sum of the first four terms of a. GP is 20 . " we get

a  +  ar  + ar^2  +ar^3 = 20

a (  1  + r  + r^2  + r^3 ) = 20

a (  1  + r^2  + r  + r^3 ) = 20

a [ 1 (   1  + r^2  ) + r (   1  + r^2  ) ] = 20

So,

a (  1  + r  ) (   1  + r^2  ) = 20  , Substitute value from equation 1 , we get

2 (   1  + r^2  ) = 20  

1  + r^2   = 10  

r^2   = 9

r  = ± 3

Substitute that value in equation 1 , we get

If x  =  3 , So a  = 1/2

And

If x  =  - 3 , So a  = - 1

So,  term of our given G.P.  =  - 1  , 3  ,  - 9 and 27