Evaluate recursive rules

1
EXAMPLE 1
Evaluate recursive rules
Write the first six terms of the sequence.
a. a0 1, an an 1 4
b. a1 1, an 3an 1
SOLUTION
a. a0 1
b. a1 1
a1 a0 4 1 4 5
a2 3a1 3(1) 3
a2 a1 4 5 4 9
a3 3a2 3(3) 9
a3 a2 4 9 4 13
a4 3a3 3(9) 27
a4 a3 4 13 4 17
a5 3a4 3(27) 81
a5 a4 4 17 4 21
a6 3a5 3(81) 243
2
EXAMPLE 2
Write recursive rules
Write the first six terms of the sequence.
a. 3, 13, 23, 33, 43, . . .
b. 16, 40, 100, 250, 625, . . .
SOLUTION
The sequence is arithmetic with first term a1 3
and common difference d 13 3 10.
an an 1 d
General recursive equation for an
an 1 10
Substitute 10 for d.
3
EXAMPLE 2
Write recursive rules
General recursive equation for an
2.5an 1
Substitute 2.5 for r.
4
for Examples 1 and 2
GUIDED PRACTICE
Write the first five terms of the sequence.
2. a0 162, an 0.5an 1
3. a0 1, an an 1 n
5
for Examples 1 and 2
GUIDED PRACTICE
Write a recursive rule for the sequence.
5. 2, 14, 98, 686, 4802, . . .
6. 19, 13, 7, 1, 5, . . .
So, a recursive rule for the sequence is
ANSWER
a1 19, and an an 1 6.
6
for Examples 1 and 2
GUIDED PRACTICE
Write a recursive rule for the sequence.
7. 11, 22, 33, 44, 55, . . .
So, a recursive rule for the sequence is
ANSWER
a1 11, and an an 1 11.
8. 324, 108, 36, 12, 4, . . .
So, a recursive rule for the sequence is
ANSWER