Write The Arithmetic Sequence That Has Four Arithmetic Means Between -20 And 20

Write the arithmetic sequence that has four arithmetic means between -20 and 20

 

Answer:

-20, -12, -4, 4, 12, 20

Step-by-step explanation:

By using the arithmetic formula: an = a1 + (n - 1)d you can get the arithmetic means.

First lets determine the variables.

The a1 is your first term which is -20

The an is the nth term of the sequence, in this sequence the nth term is 20 (or the last term)

The n is the number of terms which is 6

And the d is the common difference, since we dont know the common diffrence we will leave it the same so d.

Now lets substitute the value:

an = 20

a1 = -20

n = 6

an = a1 + (n - 1)d

20 = -20 + (6 - 1)d

Simplify,

20 = -20 + 5d

Combine like terms,

20 + 20 = 5d

Dont forget the sign!

40 = 5d

Divide both side by 5,

8 = d

Our common difference (d) is 8, lets check if it goes to 20

Just add the previous term with 8

a1 = -20

a2 = -12

a3 = -4

a4 = 4

a5 = 12

a6 = 20

Therefore, the common difference (d) is 8.


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