We will find the first four terms using the given description, then graph them. After that, we will write a recursive and an explicit rule for the sequence.
Graph
We will make a table to show the first four terms. Note that the first term is 5 and the common difference is 15.
Let's plot the ordered pairs (1,5), (2,20), (3,35), and (4,50).
Recursive Rule
The sequence a_n is an arithmetic sequence, with first term a_1=5 and common difference d= 15. Then we can write the recursive equation.
a_n=a_(n-1) + d ⇒ a_n=a_(n-1) + 15
The recursive rule is the recursive equation together with the first term.
Recursive Rule: a_1=5, a_n=a_(n-1) + 15
Explicit Rule
The explicit rule for an arithmetic sequence is the formula a_n=a_1 + (n-1)d. For our sequence, a_1= 5 and d= 15.
a_n= a_1 + (n-1) d ⇒ a_n= 5 + (n-1) 15
Let's simplify the right hand side of the equation.
