Let's denote the first term of the arithmetic progression as "a" and the common difference as "d".
We are given that the 4th term is 6, so we can write the equation:
a + 3d = 6 ...(1)
We are also given that the sum of the 8th and 9th term is -72, so we can write the equation:
(a + 7d) + (a + 8d) = -72
Simplifying the equation, we get:
2a + 15d = -72 ...(2)
We can solve this system of equations (equations 1 and 2) to find the values of "a" and "d".
Multiplying equation (1) by 2, we get:
2a + 6d = 12 ...(3)
Subtracting equation (3) from equation (2), we get:
(2a + 15d) - (2a + 6d) = -72 - 12
9d = -84
d = -84/9
d = -28/3
Therefore, the common difference is -28/3.
The 4th term of an arithmetic progression is 6. If the sum of the 8th and 9th term is -72, find the common difference
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