9th term of A.P. is 35 and 19th term is 75, then 20th term will be :(

1.	9th term of A.P. is 35 and 19th term is 75, then 20th term will be :(a) 78(b) 79(c) 80(d) 81
Answer» Answer is (b) 79 Given, T₉ = 35 ⇒ a + 8d = 35 …(i) and T₁₉ = 75 ⇒ a + 18d = 75 …(ii) Subtracting equation (i) from equation (ii), 10d = 40 ⇒ d = 4 Put d = 4 in equation (i), a + 8 × 4 = 35 ⇒ a + 32 = 35 ⇒ a = 35 – 32 = 3 ⇒ a = 3 Thus, 20^th term = T₂₀ = a + 19 d = 3 + 19 × 4 = 3 + 76 = 79

9th term of A.P. is 35 and 19th term is 75, then 20th term will be :(a) 78(b) 79(c) 80(d) 81

Answer»

Answer is (b) 79

Given,

T₉ = 35

⇒ a + 8d = 35 …(i)

and T₁₉ = 75

⇒ a + 18d = 75 …(ii)

Subtracting equation (i) from equation (ii),

10d = 40 ⇒ d = 4

Put d = 4 in equation (i),

a + 8 × 4 = 35

⇒ a + 32 = 35

⇒ a = 35 – 32 = 3 ⇒ a = 3

Thus, 20^th term = T₂₀

= a + 19 d

= 3 + 19 × 4 = 3 + 76 = 79