Arithmetic and Geometric Means

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

Find three arithmetic means between 1 and 4 1, ____, ____, ____, 4 1 4 5 NA x The three arithmetic means are 7 4 , 10 4 , and 13 4 since 1, 7 4 , 10 4 , 13 4 , 4 forms an arithmetic sequence

The 4th term of an arithmetic sequence is –9. The 8th term is 21. Find the first term and then 9th term. –31.5 ___ ___ ___ -9 ___ ___ ___ 21 ___ 28.5 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 21 = –9 + (8 – 4)d 21 = –9 + 4d 7.5 = d a4 = a 1 + (4 – 1)7.5 –9 = a 1 + 3(7.5) –31.5 = a 1 a 9 = 21 + 7.5 = 28.5

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

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