![]() ![]() You may wish to use graphing software such as the free-to-download Geogebra to investigate the graphs. What if the starting number for your geometric sequence is a fraction, or a negative number? What if the common ratio is a fraction, or a negative number? Here are some questions you might like to explore:Ĭan you make any predictions about the graph from the geometric sequence you use to generate the equation? Oliver's sequence starts at $1$ and has common ratio $2$ (each number in the sequence is $2$ times the previous number).Ĭreate some more geometrical sequences and substitute consecutive terms into Oliver's quadratic equation. 373 Sequences, 373376 arithmetic, 374375, 377 geometric, 386389 nth term. What is a quadratic sequence Ans Ans: There are four sorts of sequences that you should be familiar with: arithmetic sequences, geometric sequences. Oliver's sequence is an example of a geometrical sequence, created by taking a number and then repeatedly multiplying by a common ratio. 279, 280281, 668670 Quadratic discriminant, 131 Quadratic equations. ![]() In contrast, a geometric sequence is one where each term equals the one before it multiplied by a certain value. Each term in this sequence equals the term before it with 5 added on. (Notice how this is the same form as used for quadratic equations.) Any term of the. Oliver has been experimenting with quadratic equations of the form: $$y=ax^2+2bx+c$$ Oliver chose values of $a, b$ and $c$ by taking three consecutive terms from the sequence: $$1, 2, 4, 8, 16, 32.$$ Try plotting some graphs based on Oliver's quadratic equations, for different sets of consecutive terms from his sequence.Ĭan you make any generalisations? Can you prove them? An arithmetic series is one where each term is equal the one before it plus some number. Quadratic sequences The \ (nth\) term of a quadratic sequence has the form \ (an2 + bn + c\). ![]()
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