6.1 quadratic sequences and tableshisema011.4K visualizaes8 slides. In an arithmetic sequence the difference between successive terms, a(n+1) an, is always the same, the constant d in a geometric sequence the ratio of successive terms. (2) The definitions allow us to recognize both arithmetic and geometric sequences. You may wish to use graphing software such as the free-to-download Geogebra to investigate the graphs. It also presents the definition of sequence, arithmetic and geometric sequence. For a geometric sequence, a formula for the n th term of the sequence is an ar(n-1). What if the starting number for your geometric sequence is a fraction, or a negative number? y m x + b has a fariable to the power of 1, a constant rate of change and an offset. What if the common ratio is a fraction, or a negative number? y n 2 + n has a variable to a power of 2 added to the variable. 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. Oliver's sequence is an example of a geometrical sequence, created by taking a number and then repeatedly multiplying by a common ratio. 1.1.1 Write down the values of the next TWO terms of the. ![]() ![]() The derivation of the formula to the sum of. The quadratic number pattens will also be assessed in grade 12. 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? Arithmetic and Geometric number patterns or sequences 2.
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