I do not know any good way to find out what the quadratic might be without doing a quadratic regression in the calculator, in the TI series, this is known as STAT, so plugging the original numbers in, I ended with the equation:į(x) = 17.5x^2 - 27.5x + 15.
Then the second difference (60 - 25 = 35, 95-60 = 35, 130-95=35, 165-130 = 35) gives a second common difference, so we know that it is quadratic. = a ( 4 ) + 2 =a(4)+2 = a ( 4 ) + 2 equals, a, left parenthesis, 4, right parenthesis, plus, 2 = 9 =\goldD9 = 9 equals, start color #e07d10, 9, end color #e07d10Ī ( 5 ) a(5) a ( 5 ) a, left parenthesis, 5, right parenthesis = 7 + 2 =\blueD 7+2 = 7 + 2 equals, start color #11accd, 7, end color #11accd, plus, 2 = a ( 3 ) + 2 =a(3)+2 = a ( 3 ) + 2 equals, a, left parenthesis, 3, right parenthesis, plus, 2 = 7 =\blueD 7 = 7 equals, start color #11accd, 7, end color #11accdĪ ( 4 ) a(4) a ( 4 ) a, left parenthesis, 4, right parenthesis = 5 + 2 =\purpleC5+2 = 5 + 2 equals, start color #aa87ff, 5, end color #aa87ff, plus, 2 = a ( 2 ) + 2 =a(2)+2 = a ( 2 ) + 2 equals, a, left parenthesis, 2, right parenthesis, plus, 2 = 5 =\purpleC5 = 5 equals, start color #aa87ff, 5, end color #aa87ffĪ ( 3 ) a(3) a ( 3 ) a, left parenthesis, 3, right parenthesis = a ( 1 ) + 2 =a(1)+2 = a ( 1 ) + 2 equals, a, left parenthesis, 1, right parenthesis, plus, 2 = 3 =\greenE 3 = 3 equals, start color #0d923f, 3, end color #0d923fĪ ( 2 ) a(2) a ( 2 ) a, left parenthesis, 2, right parenthesis = a ( n − 1 ) + 2 =a(n\!-\!\!1)+2 = a ( n − 1 ) + 2 equals, a, left parenthesis, n, minus, 1, right parenthesis, plus, 2Ī ( 1 ) a(1) a ( 1 ) a, left parenthesis, 1, right parenthesis A ( n ) a(n) a ( n ) a, left parenthesis, n, right parenthesis Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the
In each term, the number of times a 1 a 1 is multiplied by r is one less than the number of the term. r or r 3 r 3) and in the fifth term, the a 1 a 1 is multiplied by r four times.
In the fourth term, the a 1 a 1 is multiplied by r three times ( r In the third term, the a 1 a 1 is multiplied by r two times ( r In the second term, the a 1 a 1 is multiplied by r. The first term, a 1, a 1, is not multiplied by any r. We will then look for a pattern.Īs we look for a pattern in the five terms above, we see that each of the terms starts with a 1. Let’s write the first few terms of the sequence where the first term is a 1 a 1 and the common ratio is r. Just as we found a formula for the general term of a sequence and an arithmetic sequence, we can also find a formula for the general term of a geometric sequence. Find the General Term ( nth Term) of a Geometric Sequence Write the first five terms of the sequence where the first term is 6 and the common ratio is r = −4.
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