FST Arithmetic Explicit Notes
Presentation
•
Mathematics, Other
•
10th - 12th Grade
•
Hard
Standards-aligned
Phara Cherdsuriya
Used 8+ times
FREE Resource
10 Slides • 18 Questions
1
Arithmetic & Geometric Explicit & Recursive Formulas Notes
Learn how to formulate arithmetic and geometric sequence to find nth term (or how many terms or means)
2
3
4
Terms to Know for Arithmetic Sequences
Sequence - a list of #s in a particular order
Term - each # in a sequence
Arithmetic sequence - a list of #s that each term after first is found by adding constant d
common difference - difference between 2 successive terms in arithmetic sequence; d = a2 - a1
5
Arithmetic Sequences: Finding the Next Terms
Find the next 3 terms ; 52, 43, 34
common difference; d = a2 - a1 = 43 - 52 = - 9
The next 3 terms are 25, 16, and 7
Find the next 3 terms ; -11, 2, 15
common difference; d = a2 - a1 = 2 - (-11) = 13
The next 3 terms are 28, 41, and 54
6
Multiple Choice
Find the next 3 terms in the sequence: 49, 45, 41, 37....
33, 29, 25, 21
33, 28, 25, 20
35, 31, 27, 23
33, 29, 26, 22
7
Arithmetic Sequences: Finding the nth term
an means nth term, a1 means the 1st term, and a0 means the term before the 1st term; n indicate a position. (such as 1st, 2nd, 3rd, or 100th)
an = d⋅n + a0; leave n as "n" when you write explicit formula.
11,13, 15, 17, 19
d = 2, a1 = 11, so a0 = 9;
an = 2n + 9
8
Multiple Choice
Find the nth term of...
8,11,14,17... an = dn + a0
an = 5n+3
an = 5n-2
an = 3n+5
an = -2n+5
9
Multiple Choice
Find the nth term of...
10,20,30,40... an = dn + a0
an = 3n
an = 2n
an = 4n
an = 10n
10
Fill in the Blanks
Type answer...
11
Arithmetic Recursive Formula;
a1 = #, an = an-1 + d
A rule in which one or more previous terms are used to generate the next term; an-1 means a previous term; a1 = #, an = an-1 + d
The Fibonnaci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . ;an = an-1 + an-2
1) a1 = 14; an = an-1 + 9
Find the 1st 5 terms ; 14, 23, 32, 41, 50
2) a1 = 6; an = an-1 - 5
The first 5 terms are 6, 1, -4, - 9, - 14
12
Multiple Choice
3) Find the 1st 5 terms; a1 = 354, an = an-1 + 6
354, 360, 366, 372, 378
360, 366, 372, 378, 384
366, 372, 378, 384, 390
372, 378, 384, 390, 396
354, 348, 342, 336, 330
13
Multiple Choice
4) Given the recursive formula below, determine a4.
a1 = 5
an = an-1 + 5
25
5
10
20
14
Multiple Choice
5) Write a recursive rule for each sequence. Then give the next 3 terms. {4, 11, 18, 25, 32, . . . }
a1 = 4,
an = an-1 - 7;
41, 50, 59
a1 = 4,
an = an-1 + 7;
39, 46, 53
a1 = 4,
an = 7 an-1,
123, 145, 189
a1 = 4,
an = an-1 - 6;
38, 44, 50
a1 = 4,
an = an-1 + 6;
38, 44, 50
15
Terms to Know for Geometric Sequences
Geometric sequence - a list of #s with multiplying a constant "r" pattern; 3, 6, 12, 24,...
Common ratio; r = 2nd term/1st term
16
Multiple Select
1) Determine whether the sequence is geometric. If yes, identify the common ratio and give the next 3 terms.
{6, 12, 24, 48, . . . }
Yes, geometric; r = 2
96, 192, 384
No, arithmetic; d = 6
Neither arithmetic nor geometric
56, 64, 72
17
Multiple Select
3) Determine whether the sequence is geometric. If yes, identify the common ratio and give the next 3 terms.
{-2, 10, -50, 250, . . . }
Yes, geometric; r = - 5
-1250, 6250, -31250
Yes, geometric; r = 5
Neither arithmetic nor geometric
1250, 6250, 31250
18
Multiple Select
4) Determine whether the sequence is geometric. If yes, identify the common ratio and give the next 3 terms.
{4, 8, 20, 60, . . . }
Yes, geometric; r = - 5
Yes, geometric; r = 5
Neither arithmetic nor geometric
No, it is arithmetic
19
Multiple Choice
8) Write the explicit formula for the following geometric sequence:
100, 50, 25, 12.5, ...
an= a1(r)n-1
an = 2(100)n-1
an = 100(2)n-1
an = 100(1/2)n-1
an = (1/2)(100)n-1
20
Geometric Recursive Formula; uses previous term.
a1 = #, an = r(an-1); r = a2 ÷ a1
Write a recursive rule, then find a5. {1, 5, 25, 125, . . . }
a1 = 1; an = 5(an-1); a5 = 625
Write a recursive rule, then find a5. {130, 65, 32.5, 16.25, . . . }
a1 = 130; an = 0.5(an-1); a5 = 8.125
21
Multiple Select
5) Write a recursive rule for each sequence. Then find a5. {2, - 8, 32, -128, . . . }
a1 = 4, an = an-1 - 7
a1 = 2, an = - 4( an-1)
a1 = 2, an = 4 an-1
a5 = 512
a5 = - 512
22
Multiple Select
6) Write a recursive rule for each sequence. Then find a5. {8, 24, 72, 216, . . .
a1 = 8, an = 3(an-1)
a1 = 8, an = - 3( an-1)
a1 = 8, an = 4 an-1
a5 = 648
a5 = - 648
23
Geometric Explicit: Finding the nth term;
an = a1⋅r n-1
Explicit Formula: A rule in which the nth term is defined as a function of n (Previous terms are unnecessary). We use it to find nth term or how many terms are there.
an = a1⋅r n-1; leave n - 1as "n - 1" for explicit.
15) a1 = 7 and r = 4; find a8.
Use an = a1⋅r n-1
a8 = 7(4)8-1= 7(4)7 = 114688
24
Multiple Choice
7) Write the explicit formula for the sequence given by 3, 6, 12, 24,
an= a1(r)n-1
an= 3(2)n-1
an= 3+(2)n
an= 3(2)n
an= 3+(2)n-1
25
Multiple Choice
Create the arithmetic explicit formula for the sequence:
-8, -6, -4, ...
(Hint: Write your formula and then simplify it.)
an = dn + a0
an= - 2+10n
an= -6 + 2n
an= 2n - 10
an= - 6 - 2n
26
Multiple Choice
Find the 26th term in the sequence: 20, 26, 32, 38, ...
27
Multiple Choice
Find a12 for the geometric sequence defined by the following formula:
an = 6(2)n-1
4096
24,576
2048
12,288
28
Multiple Choice
Create the arithmetic explicit formula for the sequence:
23, 7, - 9, ...
(Hint: Write your formula and then simplify it.)
an = dn + a0
an= - 16n + 39
an= -16 + 33n
an= 39n - 16
an= - 16 - 39n
Arithmetic & Geometric Explicit & Recursive Formulas Notes
Learn how to formulate arithmetic and geometric sequence to find nth term (or how many terms or means)
Show answer
Auto Play
Slide 1 / 28
SLIDE
Similar Resources on Wayground
23 questions
9.6 Vectors in Space
Presentation
•
10th - 12th Grade
21 questions
Paycheck
Presentation
•
9th - 12th Grade
20 questions
Intro to Probability: Theoretical vs. Experimental
Presentation
•
9th - 12th Grade
20 questions
Triangle Congruence - part 1
Presentation
•
9th - 12th Grade
23 questions
Inscribed Angles and Polygons in Circles
Presentation
•
9th - 12th Grade
23 questions
Angles Inside and Outside of a Circle
Presentation
•
9th - 12th Grade
20 questions
Inverse Functions Recap
Presentation
•
10th - 12th Grade
20 questions
Mixed Numbers
Presentation
•
4th - 5th Grade
Popular Resources on Wayground
24 questions
PBIS-HGMS Day 10
Quiz
•
6th - 8th Grade
10 questions
HCS SCI 03 Summer School Review 3
Quiz
•
3rd Grade
11 questions
Home Scope
Quiz
•
7th - 8th Grade
15 questions
HCS SCI 05 Summer School Assessment 3 Review
Quiz
•
5th Grade
35 questions
Lufkin Road Middle School Student Handbook & Policies Assessment
Quiz
•
7th Grade
18 questions
Geo 11.3 Area of Circles and Sectors
Quiz
•
9th - 11th Grade