Download Alg2H Date ______ 11-1, 11-2 Arithmetic and Geometric

WK #1
Alg2H
Date ________
11-1, 11-2 Arithmetic and Geometric Sequences Lesson Worksheet #1(revised’07)
Definition:
Sequence: A set of numbers that follows a pattern.
A function whose domain, the term numbers (n), is the set of natural numbers
and whose range is the set of term values (tn).
Examples:
1) A Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, . . . . . . . . . .
Pattern: _______________________________________________________________
Find t8 , the value of the 8th term.: _______
(This could be written as t(8) , the value of the term when n=8, in function notation.)
2) The sequence of triangular numbers: 1, 3, 6, 10, 15, 21, 28, . . . . . . . . .
Pattern: _______________________________________________________________
Find t8.: _______
3) An Arithmetic sequence: 3, 6, 9, . . . . . . . . .
Pattern: _______________________________________________________________
Find t4:________
Definition:
Arithmetic Sequence: A sequence in which one terms equals a constant ________________ the
preceding term.
The constant is called the common _______________________.
For the arithmetic sequence: 2, 5, 8, 11 . . . . . .
Find t20 = _______________________________________________________________
Formula:
For an Arithmetic Sequence:
tn = ___________________________________
In words: The nth terms equals the ________ term added to (________) common differences.
This formula is an equation for a ___________________ function.
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4) A Geometric Sequence: 3, 6, 12, . . . . . .
Pattern: _______________________________________________________________
Find t4:________
Definition:
Geometric Sequence: A sequence in which one term equals a constant _________________the
preceding term.
The constant is called the common _______________________.
For the geometric sequence: 3, 6, 12, . . . . . . .
Find t20 = _______________________________________________________________
Formula:
For an Geometric Sequence:
tn = ___________________________________
In words: The nth terms equals the ________ term multiplied by (________) common ratios.
This formula is an equation for a ___________________ function.
11-2 Sample problems:
1) Determine if the following sequences are Arithmetic, Geometric or neither.
If Arithmetic or Geometric, determine the 31st term. (If neither, 31st term not required)
a) 7, -4, -15, . . . . . . .
Type: ________________
t31 = _____________________________________________________________________
b) 1 , 1 , 2 ,.......
2 3 9
Type: ________________
t31 = _____________________________________________________________________
c)
7 , 3 7 , 6 7 ....
Type: ________________
t31 = _____________________________________________________________________
2) What term has the value of 34816 in the geometric sequence 17, 34 . . . . . . . . . . . . . . 34816?
(What term is 34816 in the Geometric sequence with t1 =17, and common ratio, r = 2?)
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3) Determine the number of terms in the Arithmetic Sequence: 305, 297, . . . . . . . 17
Find out which term the given number is in the indicated sequence:
4) – 1953125 in the sequence
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1
, − , 1 , ……………….(Technique to deal with negative common ratios)
25
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5) 305 in the sequence 17, 25, 33......
⇒over
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Find out which term the given number is in the indicated sequence:
6) Approximately 2270.6051 in the sequence 17, 18.02, 19.1012 ....
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