Question

If the 5th term of a G.P. is 2, then the product of its first nine terms is ______.

Options

• 256

• 1024

• 512

• 2048

Answer 1

If the 5th term of a G.P. is 2, then the product of its first nine terms is 512.

Explanation:

Pairing terms equally distant from the fifth gives product $$T_1T_9 = T_2T_8 = T_3T_7 = T_4T_6 = T_5^2$$. Thus, the product of all nine terms is $$T_5^9=2^9=512$$.