Question

Write a sequence that has six arithmetic means between 12.4 and -24.7

Answer 1

`12.4,7.1,1.8,-3.5,-8.8,-14.1,-19.4,-24.7`

Explanation:

If the sequence has six arithmetic means between 12.4 and -24.7.

Let the sequence be:

12.4,a,b,c,d,e,f, -24.7

It means we have:

First term, a=12.4

Eighth Term =-24.7

The nth term of an arithmetic sequence is obtained using the formula below.

`U_n=a+(n-1)d`

Therefore:

`U_8=-24.7=12.4+(8-1)d\\-24.7-12.4=7d\\7d=-37.1\\$Divide both sides by 7\\d=-5.3`

Therefore:

`U_n=12.4-5.3(n-1)\\U_1=12.4-5.3(1-1)=12.4\\U_2=12.4-5.3(2-1)=7.1\\U_3=12.4-5.3(3-1)=1.8\\U_4=12.4-5.3(4-1)=-3.5\\U_5=12.4-5.3(5-1)=-8.8\\U_6=12.4-5.3(6-1)=-14.1\\U_7=12.4-5.3(7-1)=-19.4\\U_8=12.4-5.3(8-1)=-24.7`

The sequence is:

`12.4,7.1,1.8,-3.5,-8.8,-14.1,-19.4,-24.7`