Is 68 a term of the A.P. 7, 10, 13,…?

1.	Is 68 a term of the A.P. 7, 10, 13,…?
Answer» Given, A.P is 7, 10, 13,… Here, a₁ = a = 7, a₂ = 10 Common difference, d = a₂ – a₁ = 10 – 7 = 3 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 = 7 + (n – 1)3 ⇒ a_n = 7 + 3n – 3 ⇒ a_n = 3n + 4 Now, To find whether 68 is a term of this A.P. or not Put a_n = 68 ∴ 3n + 4 = 68 ⇒ 3n = 68 – 4 ⇒ 3n = 64 ⇒ n = \(\frac{64}{3}\) \(\frac{64}{3}\) is not a natural number Hence, 68 is not a term of given A.P.

Answer»

Given,

A.P is 7, 10, 13,…

Here,

a₁ = a = 7,

a₂ = 10

Common difference,

d = a₂ – a₁

= 10 – 7

= 3

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 = 7 + (n – 1)3

⇒ a_n = 7 + 3n – 3

⇒ a_n = 3n + 4

Now,

To find whether 68 is a term of this A.P. or not

Put a_n = 68

∴ 3n + 4 = 68

⇒ 3n = 68 – 4

⇒ 3n = 64

⇒ n = \(\frac{64}{3}\)

\(\frac{64}{3}\) is not a natural number

Hence,

68 is not a term of given A.P.

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