Question
The fourth term of and A.P is 6.if the sum of the 8th and 9th term is -72, Find the common difference
Answers
Answered by
GPT 3.5
Let the common difference be represented by 'd'.
The fourth term of an A.P is given as a + 3d = 6 ...(1)
Here, a represents the first term.
The sum of the 8th and 9th term can be given as:
[(a + 7d) + (a + 8d)] = -72
2a + 15d = -72 ...(2)
Using equations (1) and (2), we can solve for 'd'.
Subtracting equation (1) from equation (2), we get:
2a + 15d - a - 3d = -72 - 6
a + 12d = -78 ...(3)
We can solve equations (1) and (3) to find the value of 'd'.
From equation (1):
a + 3d = 6
a = 6 - 3d ...(4)
Substituting equation (4) into equation (3):
6 - 3d + 12d = -78
9d = -84
d = -84/9
d = -28/3
Therefore, the common difference is -28/3.
The fourth term of an A.P is given as a + 3d = 6 ...(1)
Here, a represents the first term.
The sum of the 8th and 9th term can be given as:
[(a + 7d) + (a + 8d)] = -72
2a + 15d = -72 ...(2)
Using equations (1) and (2), we can solve for 'd'.
Subtracting equation (1) from equation (2), we get:
2a + 15d - a - 3d = -72 - 6
a + 12d = -78 ...(3)
We can solve equations (1) and (3) to find the value of 'd'.
From equation (1):
a + 3d = 6
a = 6 - 3d ...(4)
Substituting equation (4) into equation (3):
6 - 3d + 12d = -78
9d = -84
d = -84/9
d = -28/3
Therefore, the common difference is -28/3.