The sum of the 3 r d and the 4 t h terms of a G . P . is 60 and the product of its first three terms is 1000. If the first term of this G . P . is positive, then its 7 t h term is:

Step-by-step solution

Let the ' G . P . ' be a r , a , a r , a r 2 Given, a r · a · a r = 1000 ⇒ a 3 = 1000 ⇒ a = 10 Also, a r + a r 2 = 60 ⇒ 10 r + r 2 = 60 ⇒ r + r 2 = 6 ⇒ r 2 + r - 6 = 0 ⇒ r - 2   r + 3 = 0 So, r = 2 or r = - 3 As 1 s t term is positive ∴     r = 2 ∴   G . P . is ' 5 ' ,   ' 10 ' ,   ' 20 ' . . . . . . . Hence, 7 t h term is 5 · 2 6 = 320 .