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?
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.