Arithmetic Sequences
What is the common difference in the sequence: 3, 6, 9, 12, ...?
What is the common ratio in the sequence: 2, 6, 18, 54, ...?
3
The first term of a sequence is 2, and each term increases by 3. What is the value of the third term using a recursive rule?
8
A staircase has steps increasing by 2 cm. Is this arithmetic or geometric?
Arithemetic
An ordered list of numbers that follow a pattern or rule.
What is a sequence?
Find the 10th term of the sequence: 2, 5, 8, ...
29
What is the 5th term of the sequence: 1, 2, 4, 8, ...?
16
What is the recursive formula for the sequence: 5, 9, 13, 17, ...?
a1 = 5
an = an-1 + 4
You deposit $1000 in a bank that triples every year. What kind of sequence is this?
Geometric
The amount added to each term to get the next one.
What is the common difference?
What is the formula for the nth term of the sequence: 4, 10, 16, ...?
6n - 2
Write the formula for the nth term of the sequence: 3, 6, 12, ...
3 × 2ⁿ⁻¹
What is the recursive rule for the geometric sequence: 2, 6, 18, ...?
a1 = 2
an = an-1 * 3
You saved $100 each week, increasing by $50 weekly. How much have you save up by week 5?
300
The number you multiply by to get from one term to the next.
What is the common ratio?
If the 1st term is 7 and the common difference is 3, what is the 15th term?
49
A sequence has a 1st term of 5 and a common ratio of 3. Find the 6th term.
1215
Find the 6th term using the rule:
a1 = 3
an = an-1 + 7
38
You start a fitness plan where you do 10 push-ups on Day 1 and add 5 more each day. How many push-ups will you do on Day 5?
30
The previous term(s) and a rule for how to get the next term.
What is a recursive formula?
A sequence has a 1st term of 10 and a last term of 100. The common difference is 5. How many terms are in the sequence?
19
In a geometric sequence, the 1st term is 81 and the 4th term is 1. What is the common ratio?
1/3
If a1 = 1 and an = 3 * an-1 , what is a6?
243
A pendulum swings and each swing is 80% the length of the previous. If the first swing is 10 inches, what is the 4th?
5.12 inches
What is the difference between arithmetic and geometric sequences?
Arithmetic adds the same number each time; geometric multiplies by the same number each time.