The table below shows the number of push ups Devon does each day. At
this rate, how many push ups will he do on day 20? Please show your
work
day 1 2 3 4 5
# push ups 10 14 18 22 26
The pattern in the number of push ups Devon does each day is +4.
To find out how many push ups Devon will do on day 20, we need to find the 20th term in the sequence. We can use the formula for the nth term of an arithmetic sequence:
\[
a_n = a_1 + (n-1) \cdot d
\]
Where:
- \(a_n\) is the nth term
- \(a_1\) is the first term
- \(n\) is the term number
- \(d\) is the common difference
Substitute the values into the formula:
\[
a_{20} = 10 + (20-1) \cdot 4
\]
\[
a_{20} = 10 + 19 \cdot 4
\]
\[
a_{20} = 10 + 76
\]
\[
a_{20} = 86
\]
Therefore, Devon will do 86 push ups on day 20.