Question

the 9th term of an A.P is equal to seven times the seven term and twelfth term exceed five times third term by 2. Find the first term and the common difference

Answer 1

let a be the first term and d be the common difference
T9=a+(9-1)d
T9=a+8d
T7=a+6d
a+8d=7(a+6d)
a+8d=7a+42d
6a=-34d

T12=a+11d
T3=a+2d
a+11d=5(a+2d)+2
a+11d=5a+10d+2
4a=d-2
on putting a=-34/6
4×(-34)/6-d=-2
-22.67+2=d
-24.66=d