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Determine the arithmetic means as indicated.

Five arithmetic means between -2 and 16​


Sagot :

Answer: 1,4,7,10,13

Five arithmetic means between -2 and 16

-2, _ , _ , _ , _ , _ ,16

FORMULA WE'LL USE: d = [tex]\frac{an - ak}{n - k}[/tex]

Terms: an = last term; ak = first term; n and k = the no. of term

Given:

a₁ = -2; a₇ = 16; a₂ - a₆ = ?

d = [tex]\frac{an - ak}{n - k}[/tex]

d = [tex]\frac{16 - (-2)}{7-1}[/tex]

d = [tex]\frac{18}{6}[/tex]

d = 3

Hence, the common difference is 3. We can now find the terms between them.

a₂ = -2 + 3 = 1

a₃ = 1 + 3 = 4

a₄ = 4 + 3 = 7

a₅ = 7 + 3 = 10

a₆ = 10 + 3 = 13

1,4,7,10,13 are the missing or the terms between them.

So, -2, 1 , 4 , 7 , 10, 13 , 16.