# 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? 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

Approved by eNotes Editorial Team 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.

Approved by eNotes Editorial Team