A sequence is defined recursively using the formula . Which sequence could be generated using
this formula?

Ask by Cummings Page. in the United States

Jan 07,2025

Question

A sequence is defined recursively using the formula . Which sequence could be generated using
this formula?

Ask by Cummings Page. in the United States

Jan 07,2025

UpStudy AI · Accepted Answer

The recursive formula $$ f(n+1) = f(n) - 5 $$ defines a sequence where each term is 5 less than the previous term. This is an arithmetic sequence with a common difference of $$-5$$.

Let's evaluate the given options:

1. **Sequence:** $$1, -5, 25, -125, \ldots$$
   - **Differences:** $$-6, 30, -150, \ldots$$
   - **Analysis:** The differences are not constant. **Not consistent** with $$ f(n+1) = f(n) - 5 $$.

2. **Sequence:** $$2, 10, 50, 250, \ldots$$
   - **Differences:** $$8, 40, 200, \ldots$$
   - **Analysis:** The differences are not constant. **Not consistent** with $$ f(n+1) = f(n) - 5 $$.

3. **Sequence:** $$3, -2, -7, -12, \ldots$$
   - **Differences:** $$-5, -5, -5, \ldots$$
   - **Analysis:** The differences are constant at $$-5$$. **Consistent** with $$ f(n+1) = f(n) - 5 $$.

4. **Sequence:** $$4, 9, 14, 19, \ldots$$
   - **Differences:** $$5, 5, 5, \ldots$$
   - **Analysis:** The differences are constant at $$5$$. This follows $$ f(n+1) = f(n) + 5 $$, **not** $$ f(n+1) = f(n) - 5 $$.

**Conclusion:** The sequence $$3, -2, -7, -12, \ldots$$ is generated by the recursive formula $$ f(n+1) = f(n) - 5 $$.

**Answer:** $$3, -2, -7, -12,$$ …
The sequence $$3, -2, -7, -12, \ldots$$ is generated by the recursive formula $$ f(n+1) = f(n) - 5 $$.

A sequence is defined recursively using the formula . Which sequence could be generated using
this formula?

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