Question

The fourth term of an A.p. is equal to 3times the first term & seventh term exceeds twice the third term by 1. Find the first term & common difference

Answer 1

given :
4th term of an ap is equal to 3 times the 1 term
let the first term be a
so the fourth term=a+3d=3a
d=2a/3
and the 7th term=a+6d
and so
a+6d-2(a+2d)=1
a+6d-2a-4d=1
-a+2d=1
-a+2×2a/3=1
-a+4a/3=1
(-3a+4a)/3=1
a=3
so d =2
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