Question

The third term of an A.p. is 9 while the 11th term is -7, find the first five

terms of the A.

Answer 1

To find the first five terms of an arithmetic progression (A.P.), we need to first find the common difference (d).

We are given that the third term is 9, which we can write as: a + 2d = 9 (equation 1)
We are also given that the 11th term is -7, which we can write as: a + 10d = -7 (equation 2)

To find a and d, we can solve these two equations simultaneously.

Subtract equation 1 from equation 2:
(a + 10d) - (a + 2d) = -7 - 9
8d = -16
d = -16/8
d = -2

Substituting the value of d = -2 into equation 1:
a + 2*(-2) = 9
a - 4 = 9
a = 9 + 4
a = 13

So, the first term (a) is 13 and the common difference (d) is -2.

Now we can find the first five terms of the A.P:
The first term: a = 13
The second term: a + d = 13 + (-2) = 11
The third term: a + 2d = 13 + 2*(-2) = 13 - 4 = 9
The fourth term: a + 3d = 13 + 3*(-2) = 13 - 6 = 7
The fifth term: a + 4d = 13 + 4*(-2) = 13 - 8 = 5

Therefore, the first five terms of the A.P. are 13, 11, 9, 7, and 5.