Question

The sum of the 5th and 9th term of the AP is 72 and the sum of the 7 and 12 term of AP is 97 find the AP

Answer 1

T(5)+T(9)=72 - - - - - - - - - (1)
T(7)+T(12)=97 - - - - - - - - - (2)

T(n) =a+(n-1)d in Equation (1) implies,
(a+4d)+(a+8d)=72
2a+12d=72
Dividing both sides of the equation by 2,
a+6d=36 - - - - - - - - - - - (3)
a=36-6d - - - - - - - - - - - - (4)

T(n) =a+(n-1)d in Equation (2) implies,
(a+6d)+(a+11d)=97 - - - - - - - - - - - (5)
Substituting (3) in (5),
36+(a+11d)=97
a+11d=97-36
a+11d=61 - - - - - - - - - - - - (6)
Substituting (4) in (6)
(36-6d)+11d=61
36+5d=61
5d=61-36
5d=25
d=25/5
d=5
Substituting value of d in equation (4),
a=36-6d
a=36-6*5
a=36-30
a=6

Hence a=6 & d=5 of required AP
AP=a, a+d, a+2d, a+3d, a+4d,.........
AP=6, 6+5, 6+10, 6+15, 6+20,.........
AP= 6, 11, 16, 21, 26,........

Required AP is 6, 11, 16, 21, 26,........