Question

Given the arithmetic sequence where `a_1 = 6` and `a_5=-6`, what is `a_3`?

Answer 1

`a_3=0`

Explanation:

In an arithmetic sequence if `a_1` is the first term and common difference between a term `a_(n+1)` and the previous term `a_n` is `d`, then the relation between `a_n`, the `n^(th)` term and `a_1` is given by

`a_n=a_1+(n-1)d`

Now as `a_1=6` and `a_5=-6`

`a_5=a_1+(5-1)d` or

`-6=6+4d` or `4d=-12`

i.e. `d=-3` and hence

`a_3=6+(3-1)×(-3)`

= `6+2×(-3)`

= `6-6`

= `0`