Mathematics question...arthemitic progress

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.