Mathematics question.

Question

The ninth term of an AP is equal to 7 times the 2nd term and 12th term exceeds five times the third term by 2. Find the first term and common difference.

Answer 1

We have, A₉=7*a₂
a₁₂=5a₃+2

So,
a₉=(a+d)7
a₁₂=5(a+2d)+2

So,
a+8d=7a+7d, 

d=6a
a+11d=5a+10d+2,
d=4a+2,
2a=2,
a=1
d=6a=6

So, first term is 1 & common difference is 6.