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?
3 Answers
gsenviro | College Teacher | (Level 1) Educator Emeritus
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.
bababeta | Middle School Teacher | (Level 1) Adjunct Educator
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
:)