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An AP consists of 50 terms of which the 3rd term is 12 and the last term is 106. Find the 29th term.
The formula for nth term of an AP is aₙ = a + (n - 1) d
Here, aₙ is the nth 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, 50th 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
29th term of the AP is a₂₉ = a + (29 - 1)d
a₂₉ = 8 + (28) 2
a₂₉ = 8 + 56
a₂₉ = 64
Thus, 29th term of the AP is 64.
An AP consists of 50 terms of which the 3rd term is 12 and the last term is 106. Find the 29th term
NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 8
An AP consists of 50 terms of which the 3rd term is 12 and the last term is 106. The 29th term is 64.
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