the sum of difference of two GP . Is again a GP.

Explanation

False
Let two GP are `a,ar _(1) , ar_(1)^(2),ar_(2)^(3),***and b,br_(2),br_(2)^(2),br_(2)^(3),***`
Now , sum of two GP a+b `(ar+_(1)+br_(2)).(ar_(1)^(2)+br_(2)^(2)),…***`
Now , `(T_(2))/(T_(1))=(ar_(1)+br_(2))/(a+b)and (t_(3))/(T_(2)) =(ar_(1)^(2)+br_(2)^(2))/(ar_(1)+br_(2))`
`therefore (T_(2))/(T_(1)) ne (T_(3))/(t_(2))`
Again difference of two GP is a -b `ar_(1)-br_(2),ar_(1)^(2)-br_(2)^(2)....`
`Now (T_(2))/(T_(1))=(ar_(1)-br_(2))/(a-b) and (t_(3) )/(t_(2))=(ar_(1)^(2) -br_(2)^(2))/(ar_(1)-br_(2))`
`therefore (t_(2))/(T_(1))ne (T_(3))/(t_(2))`
So , the sum or difference of two GP is not a GP .
Hence m the statement is false.