arithmetic sequences
Presentation
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Mathematics
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8th - 10th Grade
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Practice Problem
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Medium
Standards-aligned
mark weinrub
Used 325+ times
FREE Resource
10 Slides • 3 Questions
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arithmetic sequences
recursive and explicit and linear
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sequences have patterns using the four operations + - x /
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Linear sequences are like lines with that y=mx+b formula you are all familiar with.
notice the pattern between the
y values, when looking at sequences it is like we are only going to look at the y values. We should assume the x values are constant or rewrite the table to make them constant and in numerical order.
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here we have the same formula but it is written AN+B.
in sequences we use the letter N to represent what term we are looking at. the first term is when n=1, the second term is when n=2, and so on. think of it like when x=1 on a graph.
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Look at the first sequence, 8 10 12 14.
remember these are like looking at the Y values. this is like when x=1, y=8. when x=2, y=10 and so on. we see a difference of +2 between y values. that difference is our slope, so we know the formula is y=2x or 2n. but what is our b? when x=0 is how we find B in graphing. we know the pattern, so if we subtract 2 from our first value, 8, that should give us the value of b. y=2x+6 or 2n+6
we now have our formulas.
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look at the second sequence, 7 11 15 19.
if you are not sure what the pattern is, try subtracting the first term from the second. 11-7=4. then check that +4 works as a common difference between all numbers in the pattern. we see it does and subtracting 4 from the first term will give us b for our formulas. 7-4=3
y=4x+3 or 4n+3
Are you ready to try?
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Multiple Choice
what is the linear equation of sequence 10 15 20 25 ?
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Multiple Choice
what is the sequence formula of 8 6 4 2 ?
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we also have special sequence formulas to learn
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we call sequences arithmetic when the common difference is adding a constant real number.
We can use these formulas when we want to know a specific term in our sequence. Like what is the 29th term or 105th term. The tiny n represents what term we want or are looking at.
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An explicit formula is used when we know the common difference and the first term and we want to know any term in the sequence.
a recursive formula is used when when we want to know what term comes next from the given term.
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Here is an arithmetic sequence 5 8 11 14.
What term comes next? we can use the recursive formula: An=An-1 + D.
An-1 is 14 and D is 3, so An=14+3=17
17 is the next term.
What is the 10th term? we can use the explicit formula: An=A1+(n-1)D
A1=first term=5 D=3 and the n we want is 10. so A10= 5 +(10 - 1) * 3
A10 = 5 + 9 * 3 = 5 + 27 = 32
the 10th term in the sequence is 32 .
ready to try one?
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Multiple Choice
what is the 101th term in this sequence of 3 5 7 9 ?
Hint: An=A1+(n-1)d
arithmetic sequences
recursive and explicit and linear
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