Question

b. The sum of the first three terms of an AP is 33. If the product of the first and the third term
exceeds the second term by 29, find the AP.​

Answer 1

Step-by-step explanation:

Let the first term be a ,

The common difference be d .

Then the sum of first three terms = a+a+d+a+2d = 3a+3d .

Given 3(a+d) = 33

=> a+d = 11 .

=> d =11-a

Therefore ,Second term of A.P = 11 .

The product of first and third terms = (a)(a+2d) = a(a+2(11-a)

= a(a+22-2a)

= a(22-a)

= 22a-a²

ATQ --->

Given 22a-a²-29= a+d

=> 22a-a²-29=11

=> 22a-a² -40 =0

=> a²-22a+40=0

=> a²-20a-2a+40=0

=> a(a-20)-2(a-20) =0

=> a= 2 or 20.

Finding common difference for a = 2

11-2=9

Finding Common difference for a =20

11-20=-9 .

Now The possible A .P 's are

1) 2,11,20,29,38,47,56,65,74.....

2) 20,11,2,-7,-16,-25,-34,-43,-52,-61,-70 .......