Question

Which of the following number(s) represents one of the 4 geometric means inserted between 2 and 486.

• A. 6
• B. 18
• C. 54
• D. 172

Answer 1

Answer: (A), (B), (C)

54

If n geometric means are inserted between a and b, then the common ratio r is
$r={\left(\frac{b}{a}\right)}^{\frac{1}{n+1}}\mathrm{Here}a=2,b=486,\mathrm{and}n=4\therefore r={\left(\frac{486}{2}\right)}^{\frac{1}{4+1}}={\left(343\right)}^{\frac{1}{5}}={\left(3^5\right)}^{\frac{1}{5}}=3.$
Hence, the four geometric means between 2 and 486 are 6, 18, 54, 162.