Show NAME ______________________________________________ DATE______________________________ PERIOD ______________3-6 PracticeArithmetic Sequences as Linear FunctionsDetermine whether each sequence is an arithmetic sequence. Writeyesorno. Explain.1.21, 13, 5, –3, ...2.–5, 12, 29, 46, ...3.–2.2, –1.1, 0.1, 1.3, ...Yes , there is commonyes , there is commonno , no common differencedifference of -8difference of 174.1, 4, 9, 16, ...5.9, 16, 23, 30, ...6.–1.2, 0.6, 1.8, 3.0, ...No , no common differenceyes , there is commonno , no common differencedifference of 7Find the next three terms of each arithmetic sequence.7.82, 76, 70, 64, ...8.–49, –35, –21, –7, ...9.34,12,14, 0, ...58 , 52 , 467 , 21 , 35-1/4 , -1/2 , -3/410.–10, –3, 4, 11 ...11.12, 10, 8, 6, ...12.12, 7, 2, –3, ...18 , 25 , 324 , 2 , 0-8 . -13 , -18Write an equation for thenth term of each arithmetic sequence. Then graph the first five terms of the sequence. How do you write an arithmetic sequence as a linear function?An arithmetic sequence is a linear function. Instead of y=mx+b, we write an=dn+c where d is the common difference and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by adding the common difference to the previous term is ak+1=ak+d.
What is the formula for a linear sequence?It is possible to determine a formula for linear sequences, i.e. sequences where the difference between successive terms is always the same. would have led to the formula un = 3n + 35. yields the formula un = 3n – 10. where the adjustment constant c may be either positive or negative.
What is the explicit rule for the arithmetic sequence an N 1?The explicit formula for the nth term of an arithmetic sequence is an = a1 + d(n - 1), where an is the nth term of the sequence, a1 is the first term of the sequence, and d is the common difference of the sequence.
How do you find the nth term of an arithmetic sequence?Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.
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Arithmetic sequences as linear functions worksheet answer key
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