# How do you write the first five terms of the sequence defined recursively #a_1=25, a_(k+1)=a_k-5#, then how do you write the nth term of the sequence as a function of n?

##### 2 Answers

We obtain general form for the equation of Arithmetic Progression from the reference:

We are given

#a_k = 30 - 5k# ,#k = 1, 2, . . . , n#

#=> ul(a_n = 30 - 5n)#

Well, the **five less** than the current term,

#25, 20, 15, 10, 5, 0, -5, . . . #

This is very similar to the graph

graph{-5x [-30.45, 42.63, -7.54, 28.97]}

In the graph, we analogously have:

#y = 25, 20, 15, 10, 5, 0, -5, . . . #

#x = -5, -4, -3, -2, -1, 0, 1, . . . #

This means the

#color(blue)(a_k = 30 - 5k, k = 1, 2, 3, . . . , n)#