Arithmetic Basics
What is the common difference in the sequence 5, 9, 13, 17...?
4
What is the common ratio in the sequence 2, 6, 18, 54...?
3
What does the “n” represent in an explicit formula?
The position (term number) in the sequence.
What does the term an−1 mean in a recursive formula?
The previous term in the sequence.
Identify whether the sequence 2, 5, 8, 11 is arithmetic or geometric.
Arithmetic
Find the 10th term of the sequence 3, 7, 11, 15...
39
Find the 5th term of the sequence 4, 12, 36, 108...
Write the explicit formula for an arithmetic sequence with a(1)=4 and d=−2.
an=4+(n−1)(−2)
Write the recursive formula for the arithmetic sequence: 2, 7, 12, 17...
an=an−1+5
Identify whether the sequence 81, 27, 9, 3 is arithmetic or geometric.
Geometric
If the 1st term of an arithmetic sequence is 12 and the common difference is -3, what is the 8th term?
-9
If the 1st term is 10 and the common ratio is ½, what is the 6th term?
10/32 or 5/16 =0.3125
Write the explicit formula for a geometric sequence with a(1)=7 and r=5.
an=7 ⋅ 5^n−1
Write the recursive formula for the geometric sequence: 3, 6, 12, 24...
an=an−1 ⋅ 2
Which type of formula (explicit or recursive) is better for finding the 100th term of a sequence?
Explicit
Write the explicit formula for the sequence: 2, 5, 8, 11...
an=2+(n−1)(3)
Write the explicit formula for the sequence: 5, 15, 45, 135...
an=5 ⋅3^n−1
Find the 15th term using the explicit formula: an=3n+1
46
A recursive sequence is defined as:
a1=10, an=an−1−4.
Find a(7)
-14
If a sequence is arithmetic with a1=6 and d=10, find the 20th term.
196
A sequence has a(1)=7 and a(12)=40. Find the common difference.
3
A geometric sequence has a1=9 and a3=36. Find the common ratio.
r = 2
The explicit formula of a sequence is:
an= 2 ⋅ (−3)^n−1. Find a(6)
-486
A recursive sequence is given by
a1=5, an=an−1⋅(−2).
Find a(6)
-160