Attempt of the following sub questions:
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 34^th term.

n^th term of A.P is given by t_n = a + (n – 1) × d

where ‘a’ is the first term of AP and ‘d’ is the common difference

given: 11^th term i.e. t₁₁ = 16 and 21^st term i.e. t₂₁ = 29

t₁₁ = 16

⇒ a + (11 – 1) × d = 16

⇒ a + 10d = 16

⇒ a = 16 – 10d …(i)

t₂₁ = 29

⇒ a + (21 – 1) × d = 29

⇒ a + 20d = 29

⇒ a = 29 – 20d …(ii)

From (i) and (ii)

16 – 10d = 29 – 20d

⇒ 20d – 10d = 29 – 16

⇒ 10d = 13

⇒ d = 1.3

Therefore, common difference is 1.3

Put d = 1.3 in equation (i)

⇒ a = 16 – (10 × 1.3)

⇒ a = 16 – 13

⇒ a = 3

Therefore, first term is 3

34^th term is given by t₃₄

⇒ t₃₄ = 3 + (34 – 1) × 1.3

⇒ t₃₄ = 3 + (33 × 1.3)

⇒ t₃₄ = 3 + 42.9

⇒ t₃₄ = 45.9

Therefore, 34^th term is 45.9