Question

Find the 80 th term of the following16, 21, 26, 31,

Answer 1

This is an arithmetic series

The formula for an arithmetic series is

$a_n=a_1+(n-1)d_{}$

where,

an is the nth term, in this example it's the 80th term

a1 is the first term, in this example it's 16

n is the term position, n = 80 in this case

and, d is the common difference between terms, in this example, this is 5 because: 31-26= 5, 26-21=5 and so on

Now, let's replace the above

$\begin{gathered} a_{80}=16+(80-1)\cdot5 \\ =16+79\cdot\: 5 \\ =16+395 \\ =411 \end{gathered}$

Thus, the 80th term is 411