Let d(n) denote the number of divisors of n i | vedclass

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(C) The number of divisors $d(n)$ for $n = p_1^{a} 	imes p_2^{b} 	imes \dots$ is given by $(a+1)(b+1) \dots$ \ $225 = 3^2 	imes 5^2 \Rightarrow d(

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in $GP$

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(C) The number of divisors $d(n)$ for $n = p_1^{a} 	imes p_2^{b} 	imes \dots$ is given by $(a+1)(b+1) \dots$ \ $225 = 3^2 	imes 5^2 \Rightarrow d(225) = (2+1)(2+1) = 3 	imes 3 = 9$ \ $1125 = 3^2 	imes 5^3 \Rightarrow d(1125) = (2+1)(3+1) = 3 	imes 4 = 12$ \ $640 = 2^7 	imes 5^1 \Rightarrow d(640) = (7+1)(1+1) = 8 	imes 2 = 16$ \ The sequence is $9, 12, 16$. \ Check for $GP$: $\frac{12}{9} = \frac{4}{3}$ and $\frac{16}{12} = \frac{4}{3}$. \ Since the common ratio is constant, $9, 12, 16$ are in $GP$.

Let $d(n)$ denote the number of divisors of $n$ including $1$ and itself. Then, $d(225)$, $d(1125)$, and $d(640)$ are

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