# An arithmetic sequence has a common difference of 9 and a(41) = 25. Find a rule for this...

## Question:

An arithmetic sequence has a common difference of 9 and a(41) = 25. Find a rule for this arithmetic sequence.

## Arithmetic Sequence Rule:

The arithmetic sequence rule is the equation of the nth term ({eq}\displaystyle a_n {/eq}) of the sequence. The arithmetic sequence formula for the nth term is $$\displaystyle a_n=a_1+(n-1)d$$ where {eq}\displaystyle a_1 {/eq} is the first term, {eq}\displaystyle n {/eq} is the term position, and {eq}\displaystyle d {/eq} is the common difference.

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Given:

• nth term, {eq}\displaystyle a_{41}=25 {/eq}
• term position, {eq}n=45 {/eq}
• common difference, {eq}\displaystyle d=25 {/eq}

From there, we...

Writing Rules for Arithmetic Sequences

from

Chapter 9 / Lesson 7
39K

Understand what an arithmetic sequence is and discover how to solve arithmetic sequence problems using the explicit and recursive formulas. Learn the formula that explains how to sum a finite number of terms of an arithmetic progression.