Respuesta :

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!

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