Question

The sum of three numbers in arithmetic progression is 51 and the product of first and third terms is 273. The common difference is:
1. 5
2. 4
3. 3
4. 6

Answer 1

Correct Answer - Option 2 : 4

Concept:

If a, b, c are in arithmetic progression (AP) then

a + c = 2b

Calculation:

Let the three terms of AP are

a - d, a, a + d

According to question,

a - d + a + a + d = 51

⇒ 3a = 51

⇒ a = 17    ----(1)

Also, according to question

(a - d)(a + d) = 273

∵ (x - y)(x + y) = x² - y²

⇒ a² - d² = 273

⇒ 289 - d² = 273     [from equation (1)]

⇒ d² = 16

⇒ d = 4