The 8th term of a series in A.P. is 23 and the 102th term is 305. Find

1.	The 8th term of a series in A.P. is 23 and the 102th term is 305. Find the series.
Answer» Let a be the first term and d be the common difference. Then, T₈ = a + (8 – 1) d ⇒ 23 = a + 7d ...(i) T₁₀₂ = a + (102 – 1) d ⇒ 305 = a + 101d ...(ii) ∴ Eqn (ii) – Eqn (i) ⇒ 94d = 282 ⇒ d = 3 Now substituting d = 3 in (i), we get 23 = a + 21 ⇒ a = 2. ∴ a = 2, d = 3 ⇒ Series is 2 + 5 + 8 + 11 + .... .

The 8th term of a series in A.P. is 23 and the 102th term is 305. Find the series.

Answer»

Let a be the first term and d be the common difference.

Then, T₈ = a + (8 – 1) d ⇒ 23 = a + 7d ...(i)

T₁₀₂ = a + (102 – 1) d ⇒ 305 = a + 101d ...(ii)

∴ Eqn (ii) – Eqn (i)

⇒ 94d = 282 ⇒ d = 3

Now substituting d = 3 in (i), we get 23 = a + 21 ⇒ a = 2.

∴ a = 2, d = 3

⇒ Series is 2 + 5 + 8 + 11 + .... .