Find the 23rd term of the arithmetic sequence. Use the drop-down lists find the common difference, to write the Explicit Formula, and to find the 23rd term.
The sequence is -4, -7, -10, -13
The common difference is -3.
The explicit formula is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
To find the 23rd term, we can substitute the values into the explicit formula:
a_23 = -4 + (23-1)(-3)
a_23 = -4 + 22(-3)
a_23 = -4 - 66
a_23 = -70
Therefore, the 23rd term of the arithmetic sequence is -70.
To find the common difference in an arithmetic sequence, we need to subtract the terms:
Common difference = -7 - (-4) = -3
The explicit formula for an arithmetic sequence is:
An = A1 + (n - 1)d
Where An represents the nth term, A1 is the first term, n is the term number, and d is the common difference.
Using the given information, we can substitute the values into the formula:
A23 = -4 + (23 - 1)(-3)
A23 = -4 + (22)(-3)
A23 = -4 + (-66)
A23 = -70
Therefore, the 23rd term of the arithmetic sequence -4, -7, -10, -13 is -70.
To find the 23rd term of an arithmetic sequence, we need to know the first term and the common difference.
In this case, the first term of the sequence is -4.
Next, let's determine the common difference. To do so, we find the difference between consecutive terms.
The difference between -4 and -7 is (-7) - (-4) = -7 + 4 = -3.
Similarly, the difference between -7 and -10 is (-10) - (-7) = -10 + 7 = -3, and the difference between -10 and -13 is (-13) - (-10) = -13 + 10 = -3.
Since each difference is -3, we can conclude that the common difference is -3.
Now that we know the common difference, we can write the explicit formula for the arithmetic sequence.
The explicit formula for an arithmetic sequence is: an = a1 + (n - 1)d, where an represents the nth term, a1 is the first term, n is the term number, and d is the common difference.
Using the values we have, the explicit formula for this arithmetic sequence is: an = -4 + (n - 1)(-3).
To find the 23rd term, substitute n = 23 in the explicit formula:
a23 = -4 + (23 - 1)(-3).
Simplifying, we have:
a23 = -4 + (22)(-3).
a23 = -4 + (-66).
a23 = -70.
Therefore, the 23rd term of the arithmetic sequence -4, -7, -10, -13 is -70.