Question

what is the 20th term of the arithmetic sequence?-8, -7, -6, -5,...

Answer 1

To find the 20th term we need to find the expression for the sequence. We know that any arithmetic sequence have the form:

$a_n=a_1+d(n-1)$

where a_1 is the first term and d is the common difference. We notice that in this case the common difference is 1. With this in mind:

$\begin{gathered} a_n=-8+1(n-1) \\ =n-9 \end{gathered}$

Hence:

$a_n=n-9$

Now that we have the sequence we can obtained the 20th term:

$a_{20}=20-9=11$

Therefore the 20th terms is 11.