Question

What must be added to each of the numbers 1, 10, 46 so that the resulting numbers are in G.P.?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

Let $x$ be the the number to be added.

Then, $x+1,x+10,x+46$ are in G.P.

$\Rightarrow (x+10{)}^2=(x+1\left)\right(x+46)$

$\Rightarrow x^2+100+20x=x^2+47x+46$

$\Rightarrow 27x=54$

$\Rightarrow x=2$

Adding 2 to the numbers 1, 10 and 46, we get 1 + 2, 10 + 2, 46 + 2=3, 12, 48, a GP with first term 3 and common ratio 4.