Question

420, 84, 16.8, 3.36,... What is the explicit rule for this sequence? An =___ *(____)^n-1

Answer 1

`a_n=420\ast(0.2)^(n-1)`

Step-by-step explanation:

The explicit formula for a geometric sequence is always given in the form;

`a_n=a_1\ast(r)^(n-1)`

where an = the nth term of the sequence

a1 = the 1st term of the sequence

r = the common ratio of the sequence

From the given sequence, we can see that the 1st term, a1, is 420.

We can find the common ratio, r, by dividing any number of the sequence with its preceding number;

`\begin{gathered} r=(84)/(420)=0.2\text{ or 16.8/84 = 0.2} \\ \therefore r=0.2 \end{gathered}`

Substituting the above values into our formula above, we'll have;

`a_n=420\ast(0.2)^(n-1)`