How do you find the three arithmetic means between 44 and 92?

Question

Theodore Amidon · Accepted Answer

#56, 68, 70#

The first method I used was Arithmetic Sequence Analysis (since the question was under "Arithmetic Sequences").

If the initial value, #44# is denoted as #a_0# then we have: #color(white)("XXX")a_0=44# #color(white)("XXX")a_1=?# #color(white)("XXX")a_2=?# #color(white)("XXX")a_3=?# #color(white)("XXX")a_4=92#

but we know that for an arithmetic sequence with initial value #a_0# and arithmetic increment #d#, the #n^(th)# value in the sequence is: #color(white)("XXX")a_n=a_0+n * d# #color(white)("XXXXXX")#Some will denote the initial value #a_1#; #color(white)("XXXXXX")#in this case the formula becomes: #color(white)("XXXXXXXXX")a_n=a_1+(n-1) * d# #color(white)("XXXXXX")#This seems unnecessarily complicated to me.

so #color(white)("XXX")a_4=92=44+4d# #color(white)("XXX")rarr d=12#

and therefore #color(white)("XXX")a_1=44+12=56# #color(white)("XXX")a_2=56+12=68# #color(white)("XXX")a_3=68+12=80#

ด ฟฟ ฟ ฟ

Method 2: Just calculate the arithmetic averages The primary arithmetic mean is the midpoint between #44# and #92# #color(white)("XXX")(44+92)/2=68#

The arithmetic mean between the initial value and the midpoint is #color(white)("XXX")(44+68)/2=56#

The arithmetic mean between the midpoint and the final value is #color(white)("XXX")(68+92)/2=80#

Serenity Johnson · Answer

undefined To find the three arithmetic means between 44 and 92, you first calculate the common difference between consecutive terms in the arithmetic sequence. Then, you add this common difference successively to the initial term (44) to find each of the arithmetic means. Finally, you have four terms: the initial term (44), the three arithmetic means, and the final term (92).