Question

Find the 32th term of a arithmetic sequence with a1=4 and d =3.

Answer 1

The nth term of a arithmetic sequence can be found with the expression below:

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

Where "an" is the nth term, "a1" is the first term, "n" is the position of the nth term and d is the ratio of the squence. Applying the data from this problem we can make n=32, a1 = 4 and d= 3 to solve for an. We have:

$\begin{gathered} a_{32}=4+(32-1)\cdot3 \\ a_{32}=4+(31)\cdot3 \\ a_{32}=4+93 \\ a_{32}=97 \end{gathered}$

The 32th term of this sequence is 97.