Question

The 11^th term and the 21^st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term. 

Answer 1

t₁₁ = 16 and t₂₁ = 29

t₁ = ?, d = ? and t₃₄ = ?

t_n = a + (n - 1) d

t₁₁ = a + (11 - 1) d

16 = a + 10 d ......(1)

t₂₁ = a + (21 - 1) d

29 = a + 20d .........(2)

Subtracting equation (1) and (2)

  a + 20 d = 29
  a + 10 d = 16
_________________
        10 d = 13

d = `13/10`

d = 1.3

Substituting d = 1.3 in equation (1)

16 = a + 10 d

a + 10 (1.3) = 16

a + 13 = 16

a = 16 - 13

a = 3

t₃₄ = 3 + (34 - 1) (1.3)

= 3 + 33(1.3)

= 3 + 42.9

t₃₄ = 45.9