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## Answers

Missing terms (arithmetic means) are: a₂, a₃, and a₄.

**Find the common difference:**

an/a₅ = 40 a₁ = 10 n = 5

an = a₁ + (n-1) (d)

40 = 10 + (5-1)(d)

40 = 10 + 4d

4d = 40 - 10

4d/4 = 30/4

**d = 15/2 ⇒ common difference (d)**

**Find the rule:**

an = 10 + (n-1) (15/2)

an = 10 + 15n/2 - 15/2

an = 15n/2 + 20/2 - 15/2

**an = 15n/2 + 5/2 ⇒ rule for the sequence (also called the nth term)**

Solve for the arithmetic means using the rule an = 15n/2 + 5/2:

a₂ = 15(2)/2 + 5/2

a₂ = 30/2 + 5/2

**a₂ = 35/2**

a₃ = 15(3)/2 + 5/2

a₃ = 45/2 + 5/2

a₃ = 50/2

**a₃ = 25**

a₄ = 15(4)/2 + 5/2

a₄ = 60/2 + 5/2

**a₄ = 65/2**

**ANSWER: The three arithmetic means are**

**35/2, 25, 65/2.**

The arithmetic sequence is:

10, 35/2, 25, 65/2, 40