Question

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

• A. in AP
• B. in HP
• C. in GP
• D. consecutive integers

Answer 1

Answer: (C)

Here, $225=3^{2} \times 5^{2}$
$\Rightarrow d(225)=3 \times 3=9$
$1125=3^{2} \times 5^{3}$
$\Rightarrow d(1125)=3 \times 4=12$
and $640=2^{7} \times 5$
$\Rightarrow d(640)=8 \times 2=16$
Hence, 9,12 and 16 are in GP.