If the sum of three numbers in G.P. is 38 and their product is 1728, what are the numbers?
1 mark
🔍 View Detailed Solution & Schema →

Question

If the sum of three numbers in G.P. is 38 and their product is 1728, what are the numbers?

Accepted Answer

Let the three numbers in G.P. be $\frac{a}{r}, a, ar$. Their product is $\frac{a}{r} 	imes a 	imes ar = a^3 = 1728$, which gives $a = 12$. Their sum is $\frac{12}{r} + 12 + 12r = 38 \Rightarrow 12(\frac{1}{r} + 1 + r) = 38 \Rightarrow \frac{1}{r} + 1 + r = \frac{19}{6} \Rightarrow \frac{1}{r} + r = \frac{13}{6}$. Solving this gives $r = \frac{2}{3}$ or $\frac{3}{2}$. The numbers are 8, 12, 18. Therefore, the correct option is B.

Sequences and Series

❓ Sibling Questions in this Chapter