Question 1031545
A sequence is a function with domain the natural numbers 1,2,3,.... Using function notation, you can write the sequence an= a1+(n-1)d as an=a1+(n-1)d and the sequence an=a1r^n-1 as a(n)=a1r^n-1
a. s a(n)=a1+(n-1)d a linear function ? Explain, if not how can you adjust its definition so that it is a linear function ? What is the slope?
a(n) = (n-1)d + a(1)
slope = (n-1)
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b.what type of function does an=a1r^n-1 suggest? To what family of functions does this function belong? explain how its related to the parent function in that family. Draw that graph.
a(n) = a(1)*r^(n-1)
Exponential
Because the exponent is n-1, the parent function is moved 1 unit to the right.
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c. what type of function is suggested by the sum sequence sn=a1(1-r^n)/1-r ?By sn= n/2 (a1 + a(n))? explan each answer
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s(n) = (n/2)*a(n) + a(1)/2
Linear with slope = (n/2) and intercept = a(1)/2
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Cheers,
Stan H.
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