Question

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
A. 13
B. 9
C. 21
D. 17

Answer 1

Answer:

13 is the write answers

Answer 2

C. 21

Step-by-step explanation:

Given: sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273

Find: 3rd term

Solution:

n = 3

S3 = 51

n/2 (a1 + a3) = 51

 3/2 (a1 + a3) = 51

a1 + a3 = 51 * 2/3

a1 + a3 = 34 -----(1)

a1 * a3 = 273  

a1 = 273/a3 ----(2)

Substituting (2) in 1, we get:

 273/a3 + a3 = 34

 Let a3 be x,

 273/x + x = 34

 273 + x² = 34x

 x² - 34x + 273 = 0

 x² - 13x -21x + 273 = 0

 x (x - 13) -21 (x -13) = 0

 X can be +13 or +21.

So the AP is 13, a2, 21......

13 + a2 + 21 = 51

So a2 = 51 - 34 = 17

 So the AP is 13, 17, 21.....

Option C is the answer.