Answers

  • Brainly User
2016-07-21T12:17:31+08:00
The arithmetic sequence is:  10,  a₂,  a₃,  a₄,  40

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

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