Homework for Friday 11-4: Finish page 83 item 19. Page 84, items 20, 3a, 3b, 3c
Today we began to use summation notation. The part to the right of the Greek letter sigma shows the rule for building the terms of the sequence based on an index, n, that increases. The part with the Greek letter sigma shows the index value for the first term (usually n=1) and the upper limit of n, the number of terms from the beginning of the sequence or series that we want to add up.
"S sub n" and sigma notation identify partial sums of a series, because we could write a series that goes on forever by generating terms of the sequences with n's that go on forever. The sum of an infinite series will be studied next year.
When we convert sigma summation notation into a series of terms, that's called expanding the notation. Sigma notation has a lot of information that we must view as a sequence or as a series in order to apply formulas for nth term, difference, and partial sum (page 84 in your notes).
The vocabulary for sequences and series connects with our everyday speech. If the current term is a sub n, then the previous term is a sub n-1 and the next term is a sub n + 1.
An arithmetic sequence features a common (constant) difference which is used to generate each successive term.
Hint for previous homework page 80, item d.
Use the formula for finding S sub n. Plug in the last term, n, and d and solve for a sub 1 the first term.
To find the nth term when given a first term, a difference, and n, use the formula
a sub n = a sub 1 + (n - 1)*d.
Use subscripts n beneath the letter a to identify which position a value or term has in a series or sequence.
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