Q33 of 36 Page 161

State whether statement in True or False.

The sum or difference of two G.P.s, is again a G.P.


Let us consider two G.P’s

a, ar, ar2, ar3, …, arn-1


and a1, a1r1, a1r12, …, a1r1n–1


Now, we will find the sum of these two G.Ps, we get


(a + a1) + (ar + a1r1) + (ar2 + a1r12) + … + (arn-1 + a1r1n-1)


Now,


and


Clearly,


So, the sum of two G.Ps is not a G.P because the common ratio is not same.


Now, we will find the difference of the two G.Ps


(a – a1) + (ar – a1r1) + (ar2 – a1r12) + … + (arn-1 – a1r1n-1)


Now,


and


Clearly,


So, the difference of two G.Ps is not a G.P because the common ratio is not same.


Hence, the given statement is FALSE


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