Question

The 9th term of an AP is equal to 7 times the second term and 12 term exceeds 5 times the third term by 3 find the first term and the common difference

Answer 1

let the first term be a and common difference be d.
a9=7a​2
a+8d =7(a+d)
-6a+d =0 ........(1)
a12=5a3+2
a+11d = 5(a+2d)+2
-4a +d = 2 ........(2)
subtrating (2) from (1)
-2a = -2
a=1
substituting in (1)
-6+d=0
d=6