How do you find the arithmetic means of the sequence 55, __, __, __, 115?

1 Answer
Jan 6, 2017

Answer:

Arithmetic Mean = #color(green)(85)#

Explanation:

Suppose the common difference is #d#
Then the first 5 terms are
[1] #a =55#
[2] #a+d=55+d#
[3] #a+2d=55+2dcolor(white)("XX")larr "middle term"#
[4] #a+3d=55+3d#
[5] #a+4d=55+4d=115#

Since #55+4d=115#
#rarr 4d=60#

#rarr d=15#

The arithmetic means (average) of an arithmetic sequence with an odd number of terms is the value of the middle term.
In this case,
#"Average" = a+2d = 55+2 * 15 = 55+30 =85#