given the recursive formula, write out the first 4 terms.
a1=7
an=an-1+3

Given the recursive formula:

- \( a_1 = 7 \)
- \( a_n = a_{n-1} + 3 \)

We can write out the first four terms as follows:

1. \( a_1 = 7 \) (This is given.)
2. \( a_2 = a_1 + 3 = 7 + 3 = 10 \)
3. \( a_3 = a_2 + 3 = 10 + 3 = 13 \)
4. \( a_4 = a_3 + 3 = 13 + 3 = 16 \)

So, the first four terms are:

\[
7, 10, 13, 16
\]

Would you like more details or have any questions?

Here are five related questions to consider:

1. What would be the 10th term in the sequence?
2. Can you express the \( n \)th term of the sequence using a direct formula (non-recursive)?
3. How would the sequence change if the recursive formula was \( a_n = a_{n-1} + 5 \)?
4. What is the common difference in the arithmetic sequence defined by the recursive formula?
5. How can you determine if a given number is part of this sequence?

**Tip:** Understanding how to convert a recursive formula to a closed-form expression can make it easier to find any term in the sequence without calculating all the previous terms.

Given the recursive formula, write out the first 4 terms.
a1=7
an=an-1+3

Learn how to find the first four terms of a recursive sequence where the first term is 7, and each subsequent term is found by adding 3 to the previous term. This example is ideal for students in Grades 6-8 and covers key algebraic concepts, including recursive formulas and arithmetic sequences.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation