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ISEE Upper Level Quantitative : Data Analysis

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Example Questions

Example Question #191 : Data Analysis And Probability

Define a sequence as follows:

$a_{1} = 3$

$a_{2} = 1$

For all integers n > 2 , $a_{n} = 3a_{n-1} - a_{n-2}$ .

Which of the following expressions is equal to $a_{1,000}$ ?

Possible Answers:

$a_{998 } -9a_{997}$

$8a_{998 } - a_{997}$

$8a_{998 } - 3 a_{997}$

$9a_{998 } - 2a_{997}$

$9a_{998 } - a_{997}$

Correct answer:

$8a_{998 } - 3 a_{997}$

Explanation:

Setting n = 1,000 :

$a_{n} = 3a_{n-1} - a_{n-2}$

$a_{1,000} = 3a_{1,000-1} - a_{1,000-2}$

$a_{1,000} = 3a_{999} - a_{998}$

Similarly,

$a_{999} = 3a_{998 } - a_{997}$

Substituting:

$a_{1,000} = 3 (3a_{998 } - a_{997}) - a_{998}$

$=9a_{998 } - 3 a_{997} - a_{998}$

$=8a_{998 } - 3 a_{997}$

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ISEE Upper Level Quantitative : Data Analysis

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #191 : Data Analysis And Probability

All ISEE Upper Level Quantitative Resources

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