In an A.P., the product of the first term and the second term is 120 and the product of the second term and the third term is 168. Find the tenth term of the A.P. when common difference d > 0.

28

In an Arithmetic Progression,

1st term × 2nd term = 120

a(a+d) = 120 .........1

2nd term × 3rd term = 168

(a+d)(a+2d) = 168  .......2

Dividing 2 by 1

(a+2d)/a = 168/120

a+2d = 1.4a

d = 0.2a

a(a+0.2a) = 120

a = +/- 10

d = +/- 0.2(10) = +/- 2 (But d>0)

Therefore, a=10 and d=2

a+9d = 10+9(2) = 28

The correct answer is Option (3) → 28