We have,
a.r^2 + a.r^3 = 60
a.r^2 (1 + r) = 60 ......(1)
Also,
a × ar × a.r^2 = 1000
(ar)^3 = (10)^3
ar = 10
a = 10/r ......(2)
Substituting this value of a in equation (1), we get
10/r × r^2 (1 + r) = 60
r(r + 1) = 6
r^2 + r - 6 = 0
r^2 + 3r - 2r - 6 = 0
r(r + 3) - 2(r + 3) = 0
(r - 2)(r + 3) = 0
r = 2, -3
Putting both the values of r in equation (1), we get
a = 10/2 and a = -10/3
a = 5, -10/3
We will take a = 5 because a is positive (according to the question).
Now,
7th term = a.r^6 = 5 × 2^6 = 5 × 64 = 320
So, the correct option is (4) 320.