# The first term of a sequence is 3 and each after the first is 2 more than the previous term. What is the expression for the nth term of the sequence for any positive integer n?

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### 3 Answers

Using the given data, the first term is 3 and the subsequent terms are 5,7,9,11,....

So the series is: 3,5,7,9,11,13,15,.......

Here `P_1` = 3

and each subsequent term differs by 2,

i.e., `P_2 - P_1 = 2`

or, `P_2 = P_1 +2`

similarly, `P_3 = P_2 + 2 = P_1 + 2*2 = P_1 + 2*(3-1)`

and so on,

thus, the nth term of the series is given by,

`P_n = 3+ 2*(n-1)`

this can also be written as

`P_n = 2n +1`

We can verify the answer by choosing any value of n

say, n=1, P1 = 2(1)+1 = 3

n=3, P3 = 2(3)+1 = 7...and so on.

Hope this helps.

The sequence would be like this

3,5,7,9,.....

The formula for finding the nth term is an = a +(n-1)d

So here first term(a) is 3 and difference (d) is constant between terms which is (5-3)=2

So nth term of this sequence is

an = 3 +(n-1)2

=3 +2n-2

=2n+1

As per the data given the first term of the sequence is

a = 3 with a common difference d = 2

so,

The sequence is as follows

3,5,7,9...........`n^(th)` term

Now we have to find the `n^(th) ` term

The above sequence is an arithmetic progression where common difference **(d) = 2**

**and a = 3**

In general, the nth term of an arithmetic progression, with first term a and common difference d, is:

nth term = `a + (n - 1)d`

= `3+ (n-1)*(2)`

= `3+2*n -2`

= `2*n +1`

is the nth term

:)

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