still need help:
Write an arithmetic sequence that has a common difference of 4 and the eighth term is 13. What is the first term? What is the 23rd term in the sequence
see earlier post
To find the first term of the arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
where:
an is the nth term,
a1 is the first term,
n is the position of the term, and
d is the common difference.
Given that the common difference (d) is 4 and the eighth term (a8) is 13, we can substitute these values into the formula and solve for a1.
a8 = a1 + (8-1)4
13 = a1 + 7(4)
13 = a1 + 28
a1 = 13 - 28
a1 = -15
Therefore, the first term (a1) of the arithmetic sequence is -15.
Next, to find the 23rd term (a23) in the sequence, we can use the same formula:
a23 = a1 + (23-1)d
Plugging in the values of the first term (a1 = -15), common difference (d = 4), and position of the term (n = 23), we can calculate the 23rd term.
a23 = -15 + (23-1)4
a23 = -15 + 22(4)
a23 = -15 + 88
a23 = 73
Therefore, the 23rd term (a23) in the arithmetic sequence is 73.
To find the first term of an arithmetic sequence, you need to use the formula:
\[ a_n = a_1 + (n - 1) \cdot d \]
Where:
- \(a_n\) is the \(n\)th term of the sequence
- \(a_1\) is the first term
- \(n\) is the position of the term in the sequence
- \(d\) is the common difference
Given that the common difference (\(d\)) is 4 and the eighth term (\(a_8\)) is 13, we can find the first term (\(a_1\)) using the formula.
Substituting the given values, we have:
\[ 13 = a_1 + (8 - 1) \cdot 4 \]
Simplifying the equation:
\[ 13 = a_1 + 7 \cdot 4 \]
\[ 13 = a_1 + 28 \]
\[ a_1 = 13 - 28 \]
\[ a_1 = -15 \]
Therefore, the first term of the arithmetic sequence is -15.
To find the 23rd term of the sequence, you can use the same formula, but substitute \(n\) with 23:
\[ a_{23} = a_1 + (23 - 1) \cdot 4 \]
Substituting the known values:
\[ a_{23} = -15 + (23 - 1) \cdot 4 \]
\[ a_{23} = -15 + 22 \cdot 4 \]
\[ a_{23} = -15 + 88 \]
\[ a_{23} = 73 \]
Therefore, the 23rd term of the arithmetic sequence is 73.