Question

Find a general function for an arithmetic sequence with a1=14
and a6=29.



an=14+(n−1)(−3)


an=14+(n−1)(9)


an=14+(n−1)(1)


an=14+(n−1)(3)

Answer 1

To find the general function for an arithmetic sequence, we need to use the formula for the \( n \)-th term of an arithmetic sequence, which is given by:

\[
a_n = a_1 + (n - 1)d
\]

where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term, and
- \( d \) is the common difference.

Given:
- \( a_1 = 14 \)
- \( a_6 = 29 \)

We can use this information to find the common difference \( d \).

1. Use the formula for \( a_6 \):

\[
a_6 = a_1 + (6 - 1)d = 14 + 5d
\]

2. Set this equal to the given value of \( a_6 \):

\[
14 + 5d = 29
\]

3. Subtract 14 from both sides:

\[
5d = 15
\]

4. Divide by 5:

\[
d = 3
\]

Now we can write the general formula for the arithmetic sequence using \( a_1 \) and \( d \):

\[
a_n = 14 + (n - 1)(3)
\]

Thus, the general function for the arithmetic sequence is:

\[
\boxed{a_n = 14 + (n - 1)(3)}
\]