Question

4th term of an AP is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. find the first term and the common differences

Answer 1

a - 3d = 3a

-3d = 2a

-3/2d = a. eq1

a - 6d = 2(a - 2d) + 1

a - 6d = 2a - 4d + 1

-a - 2d = 1 eq2

Put value of a in eq2

-(-3/2)d - 2d = 1

(3d - 4d)/2 = 1

-d = 2

d = -2

Now put d in eq1

-3/2d = a

-(3/2)*-2 = a

a = 3


Hence a = 3 and d = -2


THANKS