Download Date ___________WK#2 11-3 Arithmetic and Geometric Means

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Name __________________ Date ___________WK#2
11-3 Arithmetic and Geometric Means Lesson Worksheet #2
Definition:
Arithmetic Means between two numbers: Numbers which form an arithmetic sequence
with the two given numbers.
Geometric Means between two numbers: Numbers which form a geometric sequence with
the two given numbers.
Sample Problems:
1) Find 4 arithmetic means between 51 and 37.
2) Find one arithmetic mean between 10 and 20.
(Find the arithmetic mean of 10 and 20)
(Note: Inserting one arithmetic mean midway between the two given numbers is the same as
determining the midpoint or “average”.)
3) Find one geometric mean between 4 and 16. (Find the geometric mean of 4 and 16)
(Solve resulting quadratic by factoring)
4) Find 3 geometric means between 6 and 96, allowing the common ratio to be a complex number.
(There may be more than one set)
For r = ____ :
6, _____, ______, _______, 96
For r = ____ :
6, _____, ______, _______, 96
For r = ____ :
6, _____, ______, _______, 96
For r = ____ :
6, _____, ______, _______, 96
5) Given an arithmetic sequence with t10 = 7 and t19 = 10. Find t1 and t40
6) Find 2 geometric means between 1/9 and –3 allowing the common ratio to be a complex number.
(There may be more than one set)