Question

write an explicit formula for a_(n), the nth term of the sequence 29,37,45

Answer 1

The arithmetic sequence is given with the first term (which is a) as 29, and the common difference (which is d) as 8, that is

d=37-29

d=45-37

d=8

The explicit formular is now derived as follows;

$\begin{gathered} a_n=a+d(n-1) \\ a_n=29+8(n-1) \\ a_n=29+8n-8 \\ a_n=21+8n \end{gathered}$

The explicit formular is shown as

nth term = 21 + 8n