Question

The third term of a linear sequence (A.P)is 16 and its 6th term is 34.find the second term

Answer 1

Let's denote the first term as "a" and the common difference as "d."
The third term can be written as a + 2d, which we are given as 16.
So, a + 2d = 16. ----(1)
The sixth term can be written as a + 5d, which we are given as 34.
So, a + 5d = 34. ----(2)

To find the second term, we need to find "a" and "d."
We can solve equations (1) and (2) simultaneously to find the values of "a" and "d."

Subtracting equation (1) from equation (2), we get:
(a + 5d) - (a + 2d) = 34 - 16
3d = 18
d = 6

Now we can substitute the value of "d" in equation (1) to find "a":
a + 2d = 16
a + 2(6) = 16
a + 12 = 16
a = 16 - 12
a = 4

So, the first term "a" is 4 and the common difference "d" is 6.

To find the second term, we can use the formula:
Second term = First term + Common difference
Second term = 4 + 6
Second term = 10

Therefore, the second term of the given arithmetic progression is 10.