Question

the sum of first three terms of an APis 33.if the product of the first term and third term exceeds the 2nd term by 29 .find the APand slso find the sum of first 25terms ​

Answer 1

Answer:

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 .......