Answer :
Final answer:
To find the first three terms of an arithmetic progression (AP) using given sums of terms, we can set up equations by denoting the first term as 'a' and the common difference as 'd'. Solving the equations, we find that the first three terms of the AP are -121.75, -95, and -68.25.
Explanation:
To find the first three terms of an arithmetic progression (AP), we can use the given information about the sums of certain terms. Let's denote the first term of the AP as 'a' and the common difference as 'd'.
From the given information, we have two equations:
a + 3d + a + 7d = 24
a + 5d + a + 9d = 131
Simplifying the equations, we get:
2a + 10d = 24
2a + 14d = 131
Subtracting the first equation from the second equation, we eliminate 'a' and get:
4d = 107
Dividing both sides by 4, we find that 'd' is equal to 26.75. Substituting this value of 'd' back into the first equation, we can solve for 'a' as:
2a + 10(26.75) = 24
2a + 267.5 = 24
2a = -243.5
a = -121.75
Therefore, the first three terms of the AP are -121.75, -95, and -68.25.
