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# Two Math Questions-Thanks For Your Help :)

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1.

The explicit rule for a sequence is given.

an=1/2(4/3)^n−1

What is the recursive rule for the geometric sequence.

a1= _____   an=  ______

& 2.

Enter the explicit rule for the geometric sequence.

15,3,3/5,3/25,…

an=

Once again, thanks for your help!

Apr 5, 2018

### 1+0 Answers

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1. a1 $$-{1\over3}$$ by substituting 1 into the explicit rule.

To find the recursive rule for the sequence, note that  $$a_{n-1}={1\over2}({4\over3})^{n-1}-1$$.  Therefore:

$${4\over3}a_{n-1}={1\over2}({4\over3})^n-{4\over3}$$

$${4\over3}a_{n-1}+{1\over3}={1\over2}({4\over3})^n-1$$

$${4\over3}a_{n-1}+{1\over3}=a_n$$

To check: $$a_1=-{1\over3}$$$$a_2={1\over2}({4\over3})^2-1={4\over3}a_1+{1\over3}=-{1\over9}$$

2. Since the sequence starts at 15 and the common ratio is $$1\over3$$, the explicit rule is $$15\over5^{n-1}$$.

Apr 5, 2018

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