Question

Find the indicated term in each arithmetic sequence.

80th term of 5, 0, -5, ...

Short answer

The 80th term of the sequence is -390.

Step-by-step solution

Step 1. Given information

$\text{Thegivensequenceis}5,0,-\mathrm{5...}$

We have to find the 80th term of the sequence.

Step 2. Calculating the common difference.

Now,

$\begin{array}{l}\Rightarrow a_1=5,a_2=0,a_3=-5\\ \Rightarrow a_2-a_1=0-5=-5\\ \Rightarrow a_3-a_2=-5-0=-5\\ \Rightarrow d=-5\end{array}$

Step 3. Calculating the required term.

$\begin{array}{l}\text{The}{n}^{th}\text{termofasequenceisgivenas}\\ a_n=a_1+\left(n-1\right)d\\ \text{Here,}\\ a\text{isthefirsttermofthesequence.}\\ d\text{isthecommondifference.}\\ \text{Thus,}\\ \Rightarrow a_{80}=5+\left(80-1\right)\left(-5\right)\\ =5+79\cdot \left(-5\right)\\ =5-395\\ =-390\end{array}$