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

Jul 23, 2018

${a}_{5} = 0$

#### Explanation:

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

Therefore

${a}_{6} - {a}_{5} = {a}_{5} - {a}_{4}$

${a}_{6} + {a}_{4} = 2 {a}_{5}$

Now we can susbtitute ${a}_{4} = - {a}_{6}$ to get

${a}_{6} - {a}_{6} = 2 {a}_{5}$

$0 = 2 {a}_{5}$

${a}_{5} = 0$

Hopefully this helps!