What is the first term of an arithmetic sequence with a common difference of 5 and a sixth term of 40 ?
15
To find the first term of an arithmetic sequence, you can use the formula:
\[ a_n = a_1 + (n-1)d \]
where:
- \(a_n\) is the nth term
- \(a_1\) is the first term
- \(n\) is the position of the term
- \(d\) is the common difference
We are given that the sixth term is 40 and the common difference is 5. We can substitute these values into the formula to solve for the first term (\(a_1\)).
Using the formula:
\[ a_6 = a_1 + (6-1)d \]
Substituting the given values:
\[ 40 = a_1 + (6-1)5 \]
Simplifying the equation:
\[ 40 = a_1 + 25 \]
Subtracting 25 from both sides:
\[ 40 - 25 = a_1 \]
\[ 15 = a_1 \]
Therefore, the first term of the arithmetic sequence is 15.
To find the first term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1) * d
Where:
a_n = the nth term,
a_1 = the first term,
n = the position of the term in the sequence,
d = the common difference.
Given that the common difference (d) is 5, and the sixth term (a_6) is 40, we can substitute these values into the formula:
a_6 = a_1 + (6 - 1) * 5
Now, let's solve for a_1:
40 = a_1 + 5 * 5
40 = a_1 + 25
Subtracting 25 from both sides:
40 - 25 = a_1 + 25 - 25
15 = a_1
Therefore, the first term (a_1) of the arithmetic sequence is 15.