Question

the fourth term of an ap is equal to three times the first term and the sixth term exceeds twice the third term by 1. find the first term and common difference.

Answer 1

Dear student,
Given that,
Fourth term = 3*(First term)
a +3d = 3*(a)
2a = 3d
d = (2a)/3
Also,
Sixth term = 2*(Third term) + 1
a + 5d = 2*( a + 2d) +1
a+5d = 2a+4d+1
d = a+1
Therefore,
a+1 = (2a)/3
3a+3 = 2a
a = -3
d =a+1
d = -2