What is the third term of the sequence {eq}a_n = \dfrac{8}{n+1} {/eq}?


What is the third term of the sequence {eq}a_n = \dfrac{8}{n+1} {/eq}?

General Term of a Sequence:

We can figure out any term of a sequence if we know the formula for its general term. Given the general term {eq}a_n {/eq}, we can find the {eq}k^{\mathrm{th} } {/eq} term by substituting {eq}n=k {/eq}.

One of the types of sequences is a harmonic sequence, whose general term is obtained using:

$$a_n = \displaystyle \frac{1}{a_1+(n-1)d} $$

where the denominator is an arithmetic sequence, whose first term is {eq}a_1 {/eq} and whose common difference is {eq}d {/eq}.

Answer and Explanation:

The third term of the sequence {eq}a_n = \dfrac{8}{n+1} {/eq} is the value obtained when {eq}n=3 {/eq}.

That is, we have to plug in {eq}n =3 {/eq} to the given sequence, as shown below.

$$\begin{align*} a_n &= \dfrac{8}{n+1}\\[0.3cm] a_3 &= \dfrac{8}{3+1}\\[0.3cm] & =\bf{2} \end{align*} $$

Learn more about this topic:

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


Chapter 21 / Lesson 5

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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