Question

If an arithmetic sequence has terms a5 = 20 and a9 = 44, what is a15? 90 80 74 35

Answer 1

In order to find the 15th term of the sequence, first let's find the common rate with the formula:

$a_n=a_p+(n-p)\cdot r$

Where r is the common rate. So, using n = 9 and p = 5, we have:

$\begin{gathered} a_9=a_5+(9-5)\cdot r \\ 44=20+4\cdot r \\ 4r=44-20 \\ 4r=24 \\ r=\frac{24}{4} \\ r=6 \end{gathered}$

Then, let's use n = 15 and p = 9 to find the 15th term:

$\begin{gathered} a_{15}=a_9+(15-9)\cdot6 \\ a_{15}=44+6\cdot6 \\ a_{15}=44+36 \\ a_{15}=80 \end{gathered}$

Therefore the correct option is the second one.