The third term of an A.p. is 9 while the 11th term is -7, find the first terms of the A.
Let's denote the first term of the arithmetic progression as 'a' and the common difference as 'd'.
The third term can be expressed as:
a + 2d = 9 ------(1)
Similarly, the 11th term can be expressed as:
a + 10d = -7 ------(2)
To solve this system of equations, we can subtract equation (1) from equation (2):
(a + 10d) - (a + 2d) = -7 - 9
8d = -16
Dividing both sides of the equation by 8, we get:
d = -2
Substituting this value of d into equation (1), we can solve for a:
a + 2(-2) = 9
a - 4 = 9
a = 9 + 4
a = 13
Therefore, the first term of the arithmetic progression is 13.