Sequences and series (SL) Flashcards
What is an arithmetic sequence?
A list of numbers that change by adding or subtracting the same amount each time.
What is a “common difference, d”?
It’s the amount of increase (or decrease when negative) between terms of an arithmetic sequence.
How can you find d when given two consecutive terms (like u3 and u4) of an arithmetic series?
You subtract the terms. Always the later term minus the earlier one.
u4 - u3 = d
How can you find d when given two non-consecutive terms (like u4 and u8) of an arithmetic series?
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You set up a system of equations and solve it (with linSolve).
- Write an equation for each un you know.
- Plug these equations into linSolve.
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How can you find un if you already know u1 and d of an arithmetic series?
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You plug it into the formula from your booklet.
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What’s the difference between un and n?
- n* tells you the placement of the term. Like, 1st, 2nd, 37th, etc.
- un* is the actual value of the term.
What’s the difference between un and Sn?
- un* is the value of only the nth term
- Sn* is what you get if you add together all of the n terms.
What are context clues that you should be finding Sn?
You see these words in the question:
- calculate/find the total…
- the sum of the first n terms…
Your formula booklet has two equations for Sn of an arithmetic sequence.
Which one should you use?
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It all comes down to whether you know un or d.
- Use the first one if you only know u1 and d.
- Use the second one if you know both the 1st and last terms (u1 and un).
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What is a geometric sequence?
A list of numbers that change by multiplying (or dividing) the same amount each time.
What is a “common ratio, r”?
It’s the multiple of increase (or decrease when a fraction less than 1) between terms of a geometric sequence.
How can you find d when given two consecutive terms (like u3 and u4) of an arithmetic series?
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You divide the terms. Always the later term divided by the earlier one.
r = u4 ÷ u3
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How can you find r when given two non-consecutive terms (like u4 and u8) of an geometric series?
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You set up a system of equations and solve it (with nSolve).
- Write an equation for each un you know.
- Solve one equation for u1 by hand. (It will still have r in it).
- Substitute this equation into the other. (Now there are only rs.)
- Solve this equation with nSolve.
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How can you find un if you already know u1 and r of a geometric series?
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You plug it into the formula from your booklet.
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Your formula booklet has two equations for Sn of a geometric sequence.
Which one should you use?
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It literally makes no difference. Some people argue that one is better than the other, depending on whether r is greater or less than 1. But this is nonsense. Use either one; it doesn’t matter at all.