How do you find the arithmetic means of the sequence 10, __, __, -8?

1 Answer
Jan 10, 2017

Answer:

Arithmetic sequence is: #10, 4,-2, -8#

Explanation:

The #n^(th)# term of an arithmetic sequece s given by:

#a_n = a_1 + (n-1)*d#
Where; #a_1# is the first term and #d# is the common difference.

In this example: #a_1 =10# and #a_4 = -8#

Hence: #a_4 = a_1 + (4-1)*d#

Since #a_1= 10# and #a_4 = -8 -> 10 + (4-1)*d = -8#

#3d=-18#

#d=-6#

#:. a_2 = 10-6 = 4#

and

#a_3 = 4-6=-2#

As a check: #a_4 = -2-6 =-8#

Hence our sequence is: #10, 4,-2, -8#