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# 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 aₙ = a + (n - 1) d

Here, aₙ 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 + (3 - 1)d = a + 2d

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

Last term = 106

Thus, 50^{th} term =106 [Since, n = 50]

a + (50 - 1)d = 106

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

By solving equations (1) and (2) for the values of a and d,

a + 49d - (a + 2d) = 106 - 12

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 the AP is a₂₉ = a + (29 - 1)d

a₂₉ = 8 + (28) 2

a₂₉ = 8 + 56

a₂₉ = 64

Thus, 29^{th} term of the AP is 64.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 5

**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

**Summary:**

An AP consists of 50 terms of which the 3^{rd} term is 12 and the last term is 106. The 29^{th} term is 64.

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