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

Options

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

D

Explanation

Let a be the first term and r, the common ratio Frist nine terms of a GP are a, ar, `ar^(2),….ar^(8).`
`:." "P=a.ar.ar^(2)…ar^(8)=a^(9).r^(1+2+…+8`
`=a^(9).r^((8.9)/(2))=a^(9)r^(36=(ar^(4))^(9)=(T_(5))^(9)`
`=9th power of the 5th term