Is 302 a term of the A.P. 3, 8, 13,…?

1.	Is 302 a term of the A.P. 3, 8, 13,…?
Answer» Given, A.P is 3, 8, 13,… Here, a₁ = a = 3, a₂ = 8 Common difference, d = a₂– a₁ = 8 – 3 = 5 We know, a_n = a + (n – 1)d Where a is first term or a₁ and d is common difference and n is any natural number ∴ a_n = 3 + (n – 1)5 ⇒ a_n = 3 + 5n – 5 ⇒ a_n = 5n – 2 To find : Whether 302 is a term of this A.P. or not Put a_n = 302 ∴ 5n – 2 = 302 ⇒ 5n = 302 + 2 ⇒ 5n = 304 ⇒ n = \(\frac{304}{5}\) \(\frac{304}{5}\) is not a natural number Hence, 304 is not a term of given A.P.

Answer»

Given,

A.P is 3, 8, 13,…

Here,

a₁ = a = 3,

a₂ = 8

Common difference,

d = a₂– a₁

= 8 – 3

= 5

We know,

a_n = a + (n – 1)d

Where a is first term or a₁ and d is common difference and n is any natural number

∴ a_n = 3 + (n – 1)5

⇒ a_n = 3 + 5n – 5

⇒ a_n = 5n – 2

To find :

Whether 302 is a term of this A.P. or not

Put a_n = 302

∴ 5n – 2 = 302

⇒ 5n = 302 + 2

⇒ 5n = 304

⇒ n = \(\frac{304}{5}\)

\(\frac{304}{5}\) is not a natural number

Hence,

304 is not a term of given A.P.

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