Arithmetic Basics
What is an arithmetic sequence?
A sequence where each term increases or decreases by the same constant difference.
What does the recursive formula describe?
How to find each term from the one before it.
find the next term
What is the general explicit formula for arithmetic sequences?
an=a1+(n−1)d
What is the sum formula for arithmetic series?
Sn=n(a1+an)/2
If a1=4, d=7, what is a5?
32
What is the common difference (d) in the sequence 5, 9, 13, 17...?
4
Write a recursive rule for 2, 5, 8, 11.
an=an−1+3
Find the 10th term if a1=3, and d=2
a10=3+9(2)=21
Find the sum of the first 5 terms: 2, 5, 8, 11, 14.
S5=5(2+14)/2 =40
Which formula type uses an−1?
Recursive
Find the next 3 terms: 10, 7, 4, ...
1, -2, -5
What is the 5th term if a1=4
and an=an−1+6
28
Convert a1=7, an=an−1+5
into explicit form.
an=7+(n−1)5
Find the sum of first 10 terms if a1=3, d=2
a10=3+9(2)=21, S10=10(3+21)/2 =120
If an=2+(n-1)(5) , what is the common difference?
5
Determine if this is arithmetic: 2, 4, 8, 16.
No, it’s geometric (multiplying, not adding).
What information must be given in a recursive formula?
the common difference d
If an=−2+(n−1)(−3)
what is the 6th term?
a6=−2+(5)(-3)=−17
The 1st term is 12, 10th term is 30.
Find the sum first 10 terms.
S10=10(12+30)/2 =210
Find the 12th term and sum of first 12 terms for
a1=2, d = 3
a12=35, S12=222
is the following sequence finite or infinite?
35,40,45,50,55,...
infinite
Given a1=10 and an=an−1−4
find a7
a7=10−4(6)=−14
Find n when a1=2, d=4 , an=38
38=2+(n−1)4⇒n=10
Find the sum of the first 5 terms
The sequence starts at 6, and each term increases by 4
70
A sequence has a1=8 and a10=44
1️⃣ d=4.
2️⃣ Find the sum of the first 10 terms.
S10=10(8+44)/2=260