The sum of the first three terms of an AP is 33. If the product of the

1.	The sum of the first three terms of an AP is 33. If the product of the first and third termexceeds the 2nd term by 29. Find theAP
Answer» 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 .......

The sum of the first three terms of an AP is 33. If the product of the first and third termexceeds the 2nd term by 29. Find theAP

Answer»

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 .......