Overview:
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Using the nth term of a sequence
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Quadratic Sequences
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Limiting Values
Using the nth term of a sequence
What is the nth term of a sequence:
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This is the equation that represents each term in a sequence
The nth term equation:
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a= The first term
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d= the difference between terms
Finding out the nth term of a sequence:
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In order to find out the nth term of the sequence, we must look at our sequence and find the difference between the variables:
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Consider the sequence:
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We can see the difference between terms is 3 and the first term is 2
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Therefore we can plug these numbers into our nth term equation:
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There for our nth term is 3n + 1
Practice Question:
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Solution:
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Quadratic Sequences:
General Formula for the nth term of a quadratic sequences:
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Working out the nth term of a quadratic sequence
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Let us consider the sequence:
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In order to work the a value we must find the second difference and half it
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Here, the second difference is equal to 2, so a = 1
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In order to find the value of b, we must use the equation:
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Here we know a = 1, and the 1st difference = 8 – 3 = 5:
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In order to find c we must use the equation:
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We can substitute the values of a and b into this equation and get a value for c:
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Therefore the nth term is:
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Practice Question:
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Solution:
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Limiting Values:
What is the limiting value:
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This is the max value of a sequence when n tends to infinity
For example:
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Consider the sequence with an nth term of:
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As n tends to infinity, the –3 and +1 become negligible:
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Therefore the limiting value of the sequence is 1
