Question

The sum of the first 3 terms of an A.P. is 33.If the product of first and third term exceeds the second term by 29,find the A.P.?

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 = 211-2=9 Finding Common difference for a =2011-20=-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 ......