Answer:
general rule
an = 51 - 3 (n - 1)
a20 = -6
Explanation:
Looking at the first four terms of the series we see that each consecutive term is 3 less than the previous term. For example. 51 - 3 = 48, 48 - 3 = 45 and so on.
Therefore the general rule for the nth term is
[tex]a_n=51-3(n-1)[/tex]note that the use of using n - 1 is that when n = 1 we have
a_1 = 51 - 3(1-1) = 51 - 0 = 51
in other words, n - 1 helps us in setting a1 = 51.
Now once we have the general rule, we now find a20
[tex]a_{20}=51-3(20-1)[/tex]which simplifies to give
[tex]a_{20}=51-3\cdot19[/tex][tex]\therefore a_{20}=-6[/tex]which is our answer!
