Is any term of sequence 5, 11, 17, 23, …. will be 299?

1.	Is any term of sequence 5, 11, 17, 23, …. will be 299?
Answer» Given A.P. 5, 11, 17, 23, …….. First term (a) = 5 Common difference (d) = 11 – 5 = 6 n^th term (a_n) = 299 Formula a_n = a + (n – 1)d ⇒ 299 = 5 + (n – 1) × 6 ⇒ 299 – 5 = (n – 1) 6 ⇒ 294 = (n – 1) 6 ⇒ n – 1 = 294/6 ⇒ n – 1 = 49 ⇒ n = 49 + 1 ⇒ n = 50 n is whole no. ∴ Hence, 299 is 50^th term of sequence 5, 11, 17, 23 ….

Answer»

Given A.P.

5, 11, 17, 23, ……..

First term (a) = 5

Common difference (d) = 11 – 5 = 6

n^th term (a_n) = 299

Formula a_n = a + (n – 1)d

⇒ 299 = 5 + (n – 1) × 6

⇒ 299 – 5 = (n – 1) 6

⇒ 294 = (n – 1) 6

⇒ n – 1 = 294/6

⇒ n – 1 = 49

⇒ n = 49 + 1

⇒ n = 50

n is whole no.

∴ Hence, 299 is 50^th term of sequence 5, 11, 17, 23 ….

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