1. Arithmetic and Geometric Means

2. Find two arithmetic means between –4 and 5
-4, ____, ____, 5 -4 5 4 NA x
The two arithmetic means are –1 and 2, since –4, -1, 2, 5
forms an arithmetic sequence

3. Find three arithmetic means between 1 and 4
1, ____, ____, ____, 4 1 4 5 NA x
The three arithmetic means are 7 4 , , and 13 4
since 1, 7 4 , , , 4 forms an arithmetic sequence

4. The 4th term of an arithmetic sequence is –9.
The 8th term is Find the first term and then 9th term.
–31.5
___ ___ ___ ___ ___ ___ ___
28.5
1st 2nd rd 4th 5th th th th th
21 = –9 + (8 – 4)d
21 = –9 + 4d
7.5 = d
a4 = a 1 + (4 – 1)7.5
–9 = a (7.5)
–31.5 = a 1
a 9 = = 28.5

5. Find two geometric means between –2 and 54
-2, ____, ____, 54 -2 54 4 NA x
The two geometric means are 6 and -18, since –2, 6, -18, 54
forms an geometric sequence

6. Find one geometric mean between 1 4 and 4
𝟏 𝟒 3 NA
1 4 , 1, 4 4
1 4 , −1, 4 −4