# An AP consists of 50 terms of which the 3^{rd} term is 12 and the last term is 106. Find the 29^{th} term

**Solution:**

The formula for n^{th} term of an AP is a_{n} = a + (n - 1) d

Here, a_{n} is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

Third term of AP is a + 2d

a + 2d = 12 .... (1)

Last term = 106

50^{th} term =106

a + (50 - 1)d = 106

a + 49d = 106........ (2)

By Solving (1) & (2) for the values of a and d .

47d = 94

d = 2

Putting d = 2 in equation (1)

a + 2 × 2 = 12

a + 4 = 12

a = 12 - 4

a = 8

29^{th} term of AP is a_{29} = a + (29 - 1)d

a_{29} = 8 + (28) 2

a_{29} = 8 + 56

a_{29} = 64

Answer: 29^{th} term of AP is 64.

**Video Solution:**

## An AP consists of 50 terms of which the 3^{rd} term is 12 and the last term is 106. Find the 29^{th} term

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 8 - Chapter 5 Exercise 5.2 Question 8:

An AP consists of 50 terms of which the 3^{rd} term is 12 and the last term is 106. Find the 29^{th} term

The 29th term of the 50 terms AP whose 3rd term is 12 and the last term is 106 is 64