The 4th term of an A.P is 6.if the sum of the 8th and 9th term is 72, the common difference first term?

Answer 1

Let's denote the first term of the AP as "a" and the common difference as "d".

Given that the 4th term is 6, we can write:
a + 3d = 6 ---(1)

Also, given that the sum of the 8th and 9th term is 72, we can write:
(a + 7d) + (a + 8d) = 72
2a + 15d = 72 ---(2)

To find the value of "a" and "d", we can solve the system of equations (1) and (2).

Multiplying equation (1) by 2 gives:
2a + 6d = 12 ---(3)

Subtracting equation (3) from equation (2) gives:
2a + 15d - (2a + 6d) = 72 - 12
9d = 60
d = 60/9
d = 20/3

Substituting d = 20/3 into equation (1) gives:
a + 3(20/3) = 6
a + 20 = 6
a = 6 - 20
a = -14

Therefore, the first term of the AP is -14 and the common difference is 20/3.