We will find the first four terms of the described sequence, 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 19 and the common difference is - 13.
Let's plot the ordered pairs (1,19), (2,6), (3,- 7), and (4,- 20).
Recursive Rule
The sequence a_n is an arithmetic sequence, with first term a_1=19 and common difference d= - 13. We can write the recursive equation.
a_n=a_(n-1) + d ⇒ a_n=a_(n-1) + ( - 13)
The recursive rule is the recursive equation together with the first term.
Recursive Rule: a_1=19, a_n=a_(n-1) - 13
Explicit Rule
The explicit rule for an arithmetic sequence is the formula a_n=a_1 + (n-1)d. For our sequence a_1= 19 and d= - 13.
a_n= a_1 + (n-1) d ⇒ a_n= 19 + (n-1)( - 13)
Let's simplify the right hand side of the equation.
