The fourth term of the arithmetic-geometric progression 6,   8 ,   8 , . . . . is

Step-by-step solution

Let 6 ,   ( 6 + d ) r ,   ( 6 + 2 d ) r 2 , . . . . are in A . G . P . ⇒ 8 = 6 + d r and 8 = 6 + 2 d r 2 ⇒ 64 8 = 6 + d 2 r 2 6 + 2 d r 2 ⇒ 36 + d 2 + 12 d = 48 + 16 d ⇒ d 2 - 4 d - 12 = 0 ⇒ d = 6 , - 2 r = 8 6 + d ⇒ r = 2 3 , 2 So, the next term of the A . G . P . is 6 + 3 d r 3 = 6 + 3 × 6 2 3 3 = 24 × 8 27 = 64 9 or 6 + 3 × - 2 2 3 = 0