If 64,27,36 are the Pth Q th and R th terms of a GP, then P+2 Q is equal to

Step-by-step solution

Let a be the first term and (r ) be the common ration of a GP. ( P^ th , Q^ th ) and (R^ th ) terms of a GP are respectively ar ( ^ P -1 ), ar ( Q ⁻¹ ) and ( a r ^ R -1 ). According to question, (a r^ P-1 =64 . . ) (i) (a r^ Q-1 =27 . . ) (ii) (a r^ R-1 =36 . . ) (iii) Dividing Eq. (i) by Eq. (ii), we get ( r ^ P - Q = ( 4 3 )³ ) (iv) Dividing Eq. (ii) by Eq. (iii), we get ( array l r ^ Q - R = 3 4 r ^ 3 Q -3 R = ( 3 4 )³ array ) Multiplying Eq. (iv) and Eq. (v), we get ( array l r ^ P - Q r ^ 3 Q -3 R =1 r ^ P - Q