Question

Sum of three consecutive terms in a GP is 42 and their product is 512. Find the largest of these numbers.

• A. 32
• B. 64
• C. 128
• D. none of these

Answer 1

The correct option is A 32

Soln:

Let the three consecutive terms be$\frac{a}{r},a,ar$

Product =$\left(\frac{a}{r}\right)$(a)(ar) = $a^3$ = 512, $\Rightarrow$a = 8

Sum of these numbers$=a(1+r+\frac{1}{r})=42\Rightarrow 8(1+r+\frac{1}{r})=42$

$4r^2-17r+4=0$

(4r – 1)(r – 4) = 0

r = $\frac{1}{4}$or r = 4.

Hence the largest number is 32. The series is 32, 8, 2 or 2, 8, 32. Answer is option (a)