Question

a1 = 25, ak+1 = ak - 5how do you find the nth term of this sequence??its asking for the first 5 terms of the sequence defined recursively. It wants the pattern to write the nth term of the sequence as a function of n

Answer 1

$a_n=25-5n$

1) Considering that this sequence is defined by the following recursive formula, we can write out the following about it:

$\begin{gathered} a_1=25 \\ a_{k+1}=a_k-5 \\ a_2=a_1-5,a_2=25-5,a_2=20 \\ a_3=20-5,a_3=15 \\ a_4=15-5,a_4=10 \\ a_5=10-5,a_5=5 \\ 25,20,15,10,5. \\ \end{gathered}$

2) Note that from the recursive formula we can gather the common difference is -5.

3) Therefore, we can write out the following explicit formula:

$\begin{gathered} a_n=25-5n \\ a_n=25-5n \end{gathered}$