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lapo4ka [179]
3 years ago
6

What is the recursive rule for this geometric sequence? 3, 3/2, 3/4, 3/8

Mathematics
2 answers:
liubo4ka [24]3 years ago
8 0
I think that would be  an  = an-1 *  1/2    where an = nth term, and an-1 = previous term. 
hammer [34]3 years ago
8 0

Answer:

a_{n}=\frac{a_{n-1}}{2}

Step-by-step explanation:

Let's look a the sequence:

3, \frac{3}{2} ,\frac{3}{4} ,\frac{3}{8}

we can see that

\frac{3}{2}=3*\frac{1}{2}

and

\frac{3}{4} =\frac{3}{2}*\frac{1}{2}

and

\frac{3}{8}=\frac{3}{4}  *\frac{1}{2}

so each next number is equal to the previous number multiplied by \frac{1}{2} or, in other other words, is the previous number divided by 2.

So the recursive formula must be:

a_{n}=\frac{a_{n-1}}{2}

where a_{n} is a number in the sequence, and a_{n-1} is the immediate previous number.

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