Given the recursive formula, find a73: an = an-1 + 5 a₁ = -16

We are given the recursive formula:

\[
a_n = a_{n-1} + 5
\]
with the initial condition \(a_1 = -16\).

### To find \(a_{73}\):

This is an arithmetic sequence because the difference between consecutive terms is constant, specifically \(d = 5\). The general formula for the \(n\)-th term of an arithmetic sequence is:

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

Substituting the given values:

\[
a_{73} = a_1 + (73 - 1) \cdot 5
\]
\[
a_{73} = -16 + 72 \cdot 5
\]
\[
a_{73} = -16 + 360
\]
\[
a_{73} = 344
\]

Thus, \(a_{73} = 344\).

Would you like further details or have any questions? 

Here are 5 related questions:
1. What is the general term formula for an arithmetic sequence?
2. How do you find the sum of an arithmetic sequence?
3. What would the 100th term \(a_{100}\) be for this sequence?
4. How can you derive the recursive formula from the general formula of an arithmetic sequence?
5. What is the difference between recursive and explicit formulas?

**Tip:** In an arithmetic sequence, the recursive formula gives the relationship between consecutive terms, while the explicit formula directly calculates any term.

Given the recursive formula, find a₇₃: aₙ = aₙ₋₁ + 5, a₁ = -16

Learn how to find the 73rd term in an arithmetic sequence given the recursive formula aₙ = aₙ₋₁ + 5 and a₁ = -16. This step-by-step guide explains the process using the recursive and explicit formulas. Ideal for students in Grades 8-10.

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