The 4th term of an AP is equal to 3 times the first term and the 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.
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ATQ:
a4=3(a)
a+3d=3a
2a-3d=0 --------eq(i)
a7-2(a3)=1
a+6d-2(a+2d)=1
a+6d-2a-4d=1
-a+2d=1
a-2d=-1 -------eq(ii)
Solving eq(i) and(ii) we get
d=2 and a=3
a4=3(a)
a+3d=3a
2a-3d=0 --------eq(i)
a7-2(a3)=1
a+6d-2(a+2d)=1
a+6d-2a-4d=1
-a+2d=1
a-2d=-1 -------eq(ii)
Solving eq(i) and(ii) we get
d=2 and a=3
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