Write an equation for the nth term of the arithmetic sequence. Then graph the first five terms in the Sequence.
-3,-8,-13,-18
I got 5n-8 as my formula.
Then plugged 5 in for n and got 17 for the 5th number in the sequence.
Is this correct?
The general formula of an arithmetic sequence is
An = A1 + (n-1)d
where An refers to the nth term,
A1 refers to the first term
d refers to the common difference
Try using the above formula
Does your formula work with what was given?
To find the nth term of an arithmetic sequence, we can use the formula:
nth term = a + (n-1)d
Where:
- "nth term" represents the term number you want to find
- "a" represents the first term in the sequence
- "n" represents the term number
- "d" represents the common difference between each term
Given the arithmetic sequence: -3, -8, -13, -18
Let's find the common difference (d):
d = -8 - (-3) = -8 + 3 = -5
Now, we can find the equation for the nth term:
nth term = -3 + (n-1)(-5)
Simplifying, we have:
nth term = -3 - 5(n-1)
nth term = -3 - 5n + 5
nth term = 2 - 5n
Now, let's verify the value of the 5th term:
For n = 5:
nth term = 2 - 5(5) = 2 - 25 = -23 (not 17)
Therefore, it seems that your formula and calculation for the 5th term are incorrect.
To find the equation for the nth term of an arithmetic sequence, we need to identify the common difference between the terms. In this case, each term decreases by 5. Therefore, the common difference is -5.
Given the first term, -3, we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference.
Substituting the values, we get:
nth term = -3 + (n - 1) * (-5).
Simplifying, we have:
nth term = -3 - 5n + 5.
Combining like terms, the equation for the nth term of this arithmetic sequence is:
nth term = 2 - 5n.
Now, let's use this equation to find the first five terms of the sequence:
For n = 1,
1st term = 2 - 5(1) = 2 - 5 = -3.
For n = 2,
2nd term = 2 - 5(2) = 2 - 10 = -8.
For n = 3,
3rd term = 2 - 5(3) = 2 - 15 = -13.
For n = 4,
4th term = 2 - 5(4) = 2 - 20 = -18.
For n = 5,
5th term = 2 - 5(5) = 2 - 25 = -23.
Therefore, the first five terms in the arithmetic sequence are:
-3, -8, -13, -18, -23.
Based on this, it seems that your equation and the values you have calculated are incorrect.