Which term of the AP: 3, 8, 13, 18,…, is 78?

1.	Which term of the AP: 3, 8, 13, 18,…, is 78?
Answer» Given: 3, 8, 13, 18, …… Here a = 3; d = a₂ – a₁ = 8 – 3 = 5 Let ‘78’ be the n^th term of the given A.P. ∴ a_n = a + (n – 1) d ⇒ 78 = 3 + (n – 1) 5 ⇒ 78 = 3 + 5n – 5 ⇒ 5n = 78 + 2 ⇒ n = \(\frac{80}{5}\) = 16 ∴ 78 is the 16th term of the given A.P.

Answer»

Given: 3, 8, 13, 18, ……

Here a = 3; d = a₂ – a₁ = 8 – 3 = 5

Let ‘78’ be the n^th term of the given A.P.

∴ a_n = a + (n – 1) d

⇒ 78 = 3 + (n – 1) 5

⇒ 78 = 3 + 5n – 5

⇒ 5n = 78 + 2

⇒ n = \(\frac{80}{5}\) = 16

∴ 78 is the 16th term of the given A.P.

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