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What is the equation for an arithmetic sequence with a first term of 8 and a second term of 5?

Question:

What is the equation for an arithmetic sequence with a first term of 8 and a second term of 5?

Arithmetic Progressions

An arithmetic progression is a sequence of terms in which each two adjacent terms differ by a ratio r. Given an arithmetic sequence {eq}a_1, a_2, a_3, ..., a_n {/eq}, we may express the ratio between any two adjacent terms as {eq}r = a_2 - a_1 {/eq}, so that any term can be expressed as:

{eq}a_n = a_1 + r(n - 1) {/eq}.

Answer and Explanation: 1

In our problem:

{eq}a_1 = 8\\ a_2 = 5 {/eq}

Let's identify the ratio:

{eq}r = a_2 - a_1 = 5 - 8 = -3 {/eq}

Now, we can write a general term equation knowing that:

{eq}a_n = a_1 + r(n - 1) {/eq}

In our equation:

{eq}a_1 = 8\\ r = -3 {/eq}

So that:

{eq}a_n = 8 - 3(n - 1) = 8 - 3n + 3 = 11 - 3n {/eq}

Therefore, the general term equation for this arithmetic progression is {eq}\boxed{a_n = 11 - 3n} {/eq}.


Learn more about this topic:

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How and Why to Use the General Term of an Arithmetic Sequence

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Chapter 21 / Lesson 5
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Learn the definition of arithmetic sequence and general term of a sequence. Learn the formula for general term of a sequence and see examples.


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