Answers

2016-06-29T10:57:37+08:00
We will insert the 5 arithmetic means:

-3, a2, a3, a4, a5, a6, 12

Let a1 = -3 and a7 = 12

Getting the common difference :

a7 = a1 + 6d

Substitute the values:

12 = -3 + 6d
12 + 3 = 6d
15 = 6d
15/6 = 6d/6
d = 2 1/2

now use this:

for the 2nd term
a2 = a1 + 2 1/2 (1)
a3 = a1 + 2 1/2 (2)
a4 = a1 + 2 1/2 (3)
a5 = a1 + 2 1/2 (4)
a6 = a1 + 2 1/2 (5)

to get the arithmetic means. any clarification just ask me
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2016-06-29T14:11:47+08:00
First, find the difference:

a₁ = -3     n = 7    a₇ = 12

an = a₁ + (n - 1) d)

12 = -3 + (7-1) (d)

12 = -3 + (6)(d)

12 + 3 = 6d

6d = 15

6d/6 = 15/6

d = 5/2

The sequence are: 
-3,   -1/2,   2,   9/2,   7,   19/2,  12

(The missing 5 terms are in bold fonts)
1 5 1