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The sequence a1, a2, a3... an is an arithmetic sequence. a4=-a6. What is a5?

1 Answer

Jul 23, 2018

$a_{5} = 0$ $a_5 = 0$

Explanation:

In an arithmetic sequence a constant difference is applied to each previous term to get the next one.

Therefore

$a_{6} - a_{5} = a_{5} - a_{4}$ $a_6 - a_5 = a_5 - a_4$

$a_{6} + a_{4} = 2 a_{5}$ $a_6 + a_4 = 2a_5$

Now we can susbtitute $a_{4} = - a_{6}$ $a_4 = -a_6$ to get

$a_{6} - a_{6} = 2 a_{5}$ $a_6 - a_6 = 2a_5$

$0 = 2 a_{5}$ $0 = 2a_5$

$a_{5} = 0$ $a_5 = 0$

Hopefully this helps!

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