1. ## Arithmetic sequence

Not sure if I just don't understand the question, because I find more than one answer possible.

The question is:
Find the nth term of the arithmetic sequence: 7, 12, 17, 22,...

Possible solutions:
a) 5n+2
b) 5n+7
c) 10n+2
d) 10n+7

With (a), I get n=1, 2, 3, 4 which seems to work.
With (b), I get n=0, 1, 2, 3 which also seems to work.
With (c), I get n=.5, 1, 1.5, 2.
With (d), I get n=0, .5, 1, 1.5.

2. Originally Posted by gretchen
Not sure if I just don't understand the question, because I find more than one answer possible.

The question is:
Find the nth term of the arithmetic sequence: 7, 12, 17, 22,...

Possible solutions:
a) 5n+2
b) 5n+7
c) 10n+2
d) 10n+7

With (a), I get n=1, 2, 3, 4 which seems to work.
With (b), I get n=0, 1, 2, 3 which also seems to work.
With (c), I get n=.5, 1, 1.5, 2.
With (d), I get n=0, .5, 1, 1.5.
So you are working on the possible answers.
You are not supposed to do that. The given 4 possible answers are just for checking your work on the problem.

In an Arithmetic sequence, there is common difference, d, between successive terms. So a2 = a1 +d; a3 = a2 +d; a99 = a98 +d; ......
where a1 means 1st term, a2 = 2nd term, a99 = 99th term, ....

7, 12, 17, 22,...

Meaning, a1 = 7, a2 = 12; a3 = 17; a4 = 22
So, d = a2 -a1 = 12 -7 = 5
Or, d = a3 -a2 = 17 -12 = 5
Or, d = a4 -a3 = 22 -17 = 5
So d is really 5.

Now, a2 = a1 +d
a3 = a2 +d = (a1 +d) +d = a1 +2d ----------------> a1 +(3-1)d
a4 = a3 +d = (a1 +2d) +d = a1 +3d ---------------> a1 +(4-1)d
So,
an = a1 +(n-1)d -----***
Plugging the a1=7 and d=5 in,
an = 7 +(n-1)(5)
an = 7 +5n -5

3. Hello, Gretchen!

Either you or your teacher is goofing off.
There is a formula for this problem.

The nth term is an arithmetic sequence is: .a_n .= .a + (n-1)d

where a = first term, d = common difference, n = number of terms.

Find the nth term of the arithmetic sequence: 7, 12, 17, 22, ...

Possible solutions: . a) 5n + 2 . . b) 5n + 7 . . c) 10n + 2 . . d) 10n + 7
How hard can this be?

We have first term a = 7, common difference d = 5.

Therefore: . a_n .= .7 + (n-1)5 .= .7+ 5n - 5 .= .5n + 2