# Find the Second Term and Nth Term of an A.P. Whose 6th Term is 12 and 8th Term is 22. - Mathematics

Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22.

#### Solution

In the given problem, we are given 6th and 8th term of an A.P.

We need to find the 2nd and nth term

Here, let us take the first term as a and the common difference as d

We are given,

a_6 = 12

a_8 = 22

Now we will find a_6 and a_8 using the formula a_n = a + (n - 1)d

So

a_6 = a + (6 -1)d

12 = a + 5d  ....(1)

Also

a_8 = a + (8 -1)d

22 = a + 7d ....(2)

So to solve for a and d

On subtracting (1) from (2), we get

22 - 12 = (a + 7d) - (a + 5d)

10 = a + 7d - a - 5d

10 = 2d

d = 10/2

d = 5    ....(3)

Substituting (3) in (1) we get

12 = a + 5(5)

a = 12 - 25

a = -13

Thus

a= -13

d = 5

So, for the 2 nd term (n = 2)

a_2 = -13 + (2 - 1)5

= -13 + (1)5

= -13 + 5

= -8

For the nth term

a_n = -13 + (n - 1)5

= -13 + 5n - 5

= -18 + 5n

Therefore a_2 = -8, a_n = 5n - 18

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 15 | Page 25