Write the sequence with *n*th term:

a_{n} = 3 + 4n

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#### Solution

In the given problem, we are given the sequence with the *n*^{th} term `(a_n)`.

a_{n} = 3 + 4n

Now, to show that it is an A.P, we will first find its few terms by substituting n = 1, 2.3

So,

Substituting* n *= 1*, *we get

`a_1 = 3 + 4(1)`

`a_1 = 7`

Substituting* n *= 2*, *we get

`a_2= 3 + 4(2)`

`a_2 = 11`

Substituting* n *= 3*, *we get

`a_3 = 3 + 4(3)`

`a_3 = 15`

Further, for the given sequence to be an A.P,

Common difference (*d*) = `a_2 - a_1 = a_3 - a_2`

Here

`a_2 - a_1 = 11 - 7

= 4

Also

`a_3 - a_2 = 15 - 11`

= 4

Since `a_2 - a_1 = a_3 - a_2`

Hence, the given sequence is an A.P

Concept: Arithmetic Progression

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