Question

The product of first nine terms of a GP is, in general, equal to which one of the following?

• A. The 9th power of the 4th term
• B. The 4th power of the 9th term
• C. The 5th power of the 9th term
• D. The 9th power of the 5th term

Answer 1

Answer: (D)

The 9th power of the 5th term

Answer 2

Let a be the first term and r, the common ratio First nine terms of a GP are $a, ar, ar^2, .... ar^8$. $\therefore \, P = a.ar. ar^2 .... ar^8$ $= a^9.r^{1+2+...+8}$ $= a^9.r^{\frac{8.9}{2}}= a^9r^{36}$ $= (ar^4)^9 = (T_5)^9$ = 9th power of the 5th term