Question

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

Answer 1

`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_4 = 2a_5`

Now we can susbtitute `a_4 = -a_6` to get

`a_6 - a_6 = 2a_5`

`0 = 2a_5`

`a_5 = 0`

Hopefully this helps!