Question

Insert 6 arthematic mean between 5 and -9​

Answer 1

see explanation

Explanation:

Consider 5 and - 9 to be terms in an arithmetic sequence and we require to find the 6 terms between them.

The n th term of an arithmetic sequence is

`a_(n)` = a + (n - 1)d ← d is required

Here a = 5 and
`a_(8)` = - 9, hence

5 + 7d = - 9 ( subtract 5 from both terms )

7d = - 14 ( divide both sides by 7 )

d = - 2

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The terms in the sequence are

5, 5 - 2, 5 - 4, 5 - 6, 5 - 8, 5 - 10, 5 - 12, - 9 , that is

5, 3, 1, - 1, - 3, - 5, - 7, -9

With the 6 arithmetic means being

3, 1, - 1, - 3, - 5, - 7