Question

If the sixth term is 22 and the common difference is six what is the 50th term

Answer 1

In order to calculate the nth term of a arithmetic progression, we can use the formula:

$a_n=a_q+(n-q)r$

Where r is the ratio of the progression.

If the common difference is 6, that means the ratio is 6.

So, to find the 50th term, let's use n = 50 and q = 6 (since we know the 6th term):

$\begin{gathered} a_{50}=a_6+(50-6)\cdot6 \\ a_{50}=22+44\cdot6 \\ a_{50}=22+_{}264 \\ a_{50}=286 \end{gathered}$

So the 50th term is 286.