Math II question from Barron's

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1

<p>Hello,</p>

<p>This is first time posting here at College Confidential.
I just have a question from the Math II Barron's Book.</p>

<p>One of the examples for the Recursive Sequences was,</p>

<p>If a1 = 3 and an = 2an-1 + 5, find a4. </p>

<p><em>1, n, an-1, 4 are in small font</em></p>

<p>The answer explanation says,</p>

<p>Put 3(a1) into your graphing calculator and press ENTER. Then multiply by 2 and add 5. Hit ENTER 3 more times to get a4 = 59.</p>

<p>I don't really know what the question and the answer are saying. Where is a1 on the graphing calculator? And what is the question asking, exactly? </p>

<p>Thank you. Any help is appreciated.</p>

2

<p>a1 is referring to the first term (the subscript is the term number). This is a basic recursive sequence and a calculator would only be necessary here for ease of calculation. </p>

<p>Essentially, a recursive sequence is one where from a starting value (a1), you repeatedly apply the same process to each term to arrive at the following term. Recursion requires that you know the value of the term immediately before the term you are trying to find.</p>

<p>Thus, you would solve the above problem in the following way:</p>

<p>a1 = 3 (given)
a2 = 2(a1)+5 = 2(3)+5 = 11
a3 = 2(a2)+5 = 2(11)+5 = 27
a4 = 2(a3)+5 = 2(27)+5 = 59</p>

<p>a4 = 59</p>