Question

find the sequence whose nth term is 3+ 4n​

Answer 1

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EXPLANATION.:-

Sequence whose nth term = 3 + 4n.

As we know that,

General term of an A.P.

⇒ Tₙ = a + (n - 1)d..

⇒ 3 + 4n.

Put n = 1 in equation, we get.

⇒ 3 + 4(1).

⇒ 3 + 4

⇒ 7.

put n = 2 in equation, we get.

⇒ 3 + 4(2).

⇒ 3 + 8.

⇒ 11.

put n = 3 in equation, we get.

⇒ 3 + 4(3).

⇒ 3 + 12.

⇒ 15.

put n = 4 in equation, we get.

⇒ 3 + 4(4).

⇒ 3 + 16.

⇒ 19.

Sequence = 7, 11, 15, 19,,,,,,,,

First term = a = 7.

Common difference = d = b - a = c - b.

common difference = 11 - 7 = 15 - 11.

Common difference = 4 = 4.

Put the formula in nth term, we get.

⇒ Tₙ = a + (n - 1)d.

⇒ Tₙ = 7 + (n - 1)4.

⇒ Tₙ = 7 + 4n - 4.

⇒ Tₙ = 4n + 3.

HENCE PROVED.

Answer 2

Explanation:

Sequence whose nth term = 3 + 4n.

As we know that,

General term of an A.P.

⇒ Tₙ = a + (n - 1)d..

⇒ 3 + 4n.

Put n = 1 in equation, we get.

⇒ 3 + 4(1).

⇒ 3 + 4

⇒ 7.

put n = 2 in equation, we get.

⇒ 3 + 4(2).

⇒ 3 + 8.

⇒ 11.

put n = 3 in equation, we get.

⇒ 3 + 4(3).

⇒ 3 + 12.

⇒ 15.

put n = 4 in equation, we get.

⇒ 3 + 4(4).

⇒ 3 + 16.

⇒ 19.

Sequence = 7, 11, 15, 19,,,,,,,,

First term = a = 7.

Common difference = d = b - a = c - b.

common difference = 11 - 7 = 15 - 11.

Common difference = 4 = 4.

Put the formula in nth term, we get.

⇒ Tₙ = a + (n - 1)d.

⇒ Tₙ = 7 + (n - 1)4.

⇒ Tₙ = 7 + 4n - 4.

⇒ Tₙ = 4n + 3.

HENCE PROVED.