Question

How do you write a rule for the nth term of the arithmetic sequence and then find `a_10` for `-4, 2, 8, 14, 20`?

Answer 1

Tenth term `a_10` in given sequence is `50`.

Explanation:

In an arithmetic sequence, the difference between acreen and its immediately preceding term is always constant. This is called as 'common difference'.

Let us check here. Here, we have `2-(-4)=8-2=14-8=20-14=6`.

Hence, here we have an arithmetic sequence with first term `a_1=-4` and common difference `d` equal to `6`.

In an arithmetic sequence if first term is `a_1` and common difference is `d`, then `n(th)` term `a_n` is given by `a_n=a_1+(n-1)d`.

Hence, tenth term in given sequence is

`-4+(10-1)×6=-4+9×6=-4+54=50`.