1.2 Arithmetic sequences and seriesIB Maths: Analysis and Approaches HL: Flashcards

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What is the formula for the nth term of an arithmetic sequence?

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What is the formula for the nth term of an arithmetic sequence?: $u_n = u_1 + (n-1)d$
Give both forms of the sum of the first n terms of an arithmetic series.: $S_n = \frac{n}{2}(2u_1 + (n-1)d)$ and $S_n = \frac{n}{2}(u_1 + u_n)$
$u_4 = 17$ and $u_9 = 42$ . Find $d$ .: $5d = 25$ , so $d = 5$ .
Find $u_1$ and $d$ for $\sum_{r=1}^{n}(4r + 3)$ .: $u_1 = 7$ , $d = 4$ .
How many terms are in $\sum_{r=5}^{20} u_r$ ?: $20 - 5 + 1 = 16$ terms.
Why does simple interest produce an arithmetic sequence?: The same amount of interest (a percentage of the original sum) is added each year.
Find $S_{10}$ for $3, 7, 11, \dots$: $S_{10} = 5(6 + 36) = 210$
When solving for n in a sum, what do you do with a negative root?: Reject it — n is the number of terms, so it must be a positive integer.
Data differences are 4.1, 3.9, 4.2. What common difference might you use?: The mean difference, $\frac{4.1 + 3.9 + 4.2}{3} \approx 4.07$ .
Why is a prediction far beyond the data less reliable?: It is extrapolation; the real pattern may not continue at a constant rate.
Is $u_n = 12 - 5n$ arithmetic? What is $d$ ?: Yes, $d = -5$ (a decreasing arithmetic sequence).
If technology is used to find a sum, what must you still be able to state?: The first term and the common difference.