How many terms are in arithmetic sequence whose 1st term is -3, common difference is 2. and the last term is 23?

The formula for the \(n\)-th term of an arithmetic sequence is:

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

Where:
- \(a_n\) is the last term,
- \(a_1\) is the first term,
- \(d\) is the common difference, and
- \(n\) is the number of terms.

We are given:
- \(a_1 = -3\) (first term),
- \(d = 2\) (common difference),
- \(a_n = 23\) (last term).

Substitute these values into the formula to find \(n\):

\[
23 = -3 + (n - 1) \cdot 2
\]

Now solve for \(n\):

\[
23 + 3 = (n - 1) \cdot 2
\]
\[
26 = (n - 1) \cdot 2
\]
\[
n - 1 = \frac{26}{2} = 13
\]
\[
n = 13 + 1 = 14
\]

So, there are 14 terms in the sequence.

Would you like more details or have any questions?

Here are some related questions to explore further:
1. What is the sum of all the terms in this arithmetic sequence?
2. How would the number of terms change if the last term were 25?
3. Can you determine the 7th term of this arithmetic sequence?
4. What if the common difference was -2 instead of 2?
5. How do you calculate the common difference if only the first and last terms and number of terms are known?

**Tip:** In arithmetic sequences, the number of terms can be easily found by rearranging the general term formula!

How many terms are in an arithmetic sequence whose 1st term is -3, common difference is 2, and the last term is 23?

Learn how to find the number of terms in an arithmetic sequence where the first term is -3, the common difference is 2, and the last term is 23. This problem explains key concepts like the nth term formula for arithmetic sequences, making it suitable for students in Grades 6-8.

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