Arithmetic
What does d stand for in the following formula:
an = a1 + d(n - 1)
Common Difference
If you were to graph an arithmetic sequence, what would the graph look like?
Linear / Straight
What does r stand for in the following formula
an = a1 * r n-1
Common ratio
If you were to graph a geometric sequence, what would the graph look like?
Exponential / curvy / really big really fast
What is a recursive sequence?
A sequence defined using previous terms to calculate the next. Famous examples include the Fibonacci sequence.
a2 - a1
DESMOS TIME! Find the explicit equation of the sequence given the following graph on desmos
Explicit equation:
an = 2 + 2(n-1)
Given two terms, how can you calculate r?
a2 divided by a1
DESMOS TIME! Find the explicit equation of the sequence given the following graph on desmos
Explicit equation:
an = 2*2n-1
What two parts does every recursive sequence need?
Find the 9th term of the following sequence:
{5,9,13,17,21, ... }
37
A runner is training for a marathon using a progressive daily distance plan. Each day, she increases her running distance by the same fixed amount. On Day 8 she runs 16 miles. On Day 9 she runs 17.5 miles. What distance did she run on Day 1?
She ran 5.5 miles on day 1
Find the 9th term of the following sequence:
{5,15,45, ... }
a9 = 32,805
A tech startup launches a app with 500 active users in its first month. The user base triples every month. How many active users will the app have in its 6th month?
121,500 Active users
an = 2an-1 +1
Find the first 4 terms of the sequence
3, 7, 15, 31
Given a1 = 24 and a2 = 17, what is d?
d = -7
A movie theater row structure is designed so that Row 1 has 18 seats, Row 2 has 22 seats, and Row 3 has 26 seats. If this pattern continues, how many seats are in Row 15?
Row 15 has 74 seats
Given a1 = 24 and a2 = 3, what is r?
r = 1/8
A company buys a piece of heavy manufacturing machinery that depreciates in value over time. Each year, the machine retains $80 of its value from the previous year. If the machine is valued at $20,480 in its 5th year, what was its original purchase price?
The purchase price was $50,000
Write a recursive definition for the following sequence
5, 15, 45, 135, ...
a1 = 5
an = 3an-1
Given: d = 6 and a8 = 47, find a1
a1 = 5
A company deposits money into a reserve fund at the end of every quarter. At the end of Quarter 1 the fund $12,000. At the end of Quarter 9 after regular equal rate increases, the total balance reaches $44,000. By how much did the account balance grow each quarter?
The account grew by $4,000 each quarter
In a geometric sequence, r = 3 and a4 = 108. Find the first term a1
a1 = 4
A company purchased a delivery van for its business. Due to wear and tear, the van loses 15% of its value each year. In its 6th year of service, the van is valued at $22,185. What was the original purchase price of the van?
Original purchase price was $50,000
An explicit formula for a sequence is given by
an = 4n - 1. Express this sequence using a recursive formula
a1 = 3
an = an-1 + 4