Question

the 4th term of an ap is three times the first and the 7th term exceeds twice the third term by 1 find the first term and the common difference

Answer 1

let 'a' and 'd' be the first term and common difference of AP

given a4=3a

a+3d=3a

2a-3d=0------(1)

and a7=2a3+1

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

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

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


by solving (1) and (2)

a=3 and d=2


I hope this will help u ;)

Answer 2

1st term - a
Common difference - d

4th term = a + 3d

Given in the Question,
a + 3d = 3a
2a - 3d = 0 (1)

7th term = a + 6d
3rd term = a + 2d

Given in the Question,
a + 6d = 2( a + 2d) + 1
a + 6d = 2a + 4d + 1
a - 2d = - 1 (2)

From (1) and (2) we get,
d = 2

So a = - 1 + 4 = 3

There's your answer - 3, 2!