An AP consists of 50 terms in which the 3rd term is 12 and the last term is 106. Find the 29th term. Class 9

An AP consists of 50 terms in which the 3^rd term is 12 and the last term is 106. Find the 29^th term. Class 9

Question 1.

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

(Hint: If ’a’ is the first term and 'd' the common difference, then we arrive at the equations a + 2d = 12 and a + 49d = 106. Solve this pair of linear equations for 'a' and 'd '.) Class 9

Solution:

Given,

t₃ = 12, and t₅₀ = 106

t_n = a + (n - 1) d

For n = 3,

t₃ = a + (3 - 1) d

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

For n = 50

t₅₀ = a + (50 - 1)d

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

Subtracting (i) from (ii), we get

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

∴ a + 49d - a - 2d = 94

∴ 47d = 94

∴ d = 2

Substitute d = 2 in (i), we get

a + 2(2) = 12

∴ a = 12 - 4

∴ a = 8

For n = 29,

t₂₉ = a + (29 - 1) x d

= 8 + 28 x 2

= 8 + 56 = 64

∴ t₂₉ = 64.

∴ 29^th term of AP is 64.