This week we began learning chapter thirteen, Sequences and Series. Due to certain circumstances, we only got to learn the first section “Finite sequences and series.” I found this section to be a little difficult. And the fact that the book doesn’t give the best examples did not help either. So I’m pretty stuck until Monday when we review. Until then, I guess ill keep doing the problems until I get it.
A sequence is a list of numbers. There are two kinds of sequences : Arithmetic and Geometric. In a arithmetic sequence, the same numbers are being added. On the other hand, in a geometric sequence, the same numbers are being multiplied. Both sequences have formulas that may be used to find nth terms.
Arithmetic- t(n)= t(1) + (n-1) d * here “d” is the common difference.
Geometric- t(n) = t(1)xR^(n-1) * here “r” is the common ratio.
* if a sequence is not arithmetic or geometric, then it is “Neither.”
There are many ways you may be asked to solve sequence problems. The first way you may be asked to solve a sequence problem is to solve for the nth root. Other ways include solving for the t(n)term where the n will be given, and you may even be asked how many terms are in a given sequence.
Ex. Find the formula for t(n)
1, 4, 7, 10..
Each number is being increased by three, therefore this sequence is an Arithmetic one. The common difference is a positive four. ( d=4 ) and it uses the arithmetic formula (t(n)= t(1) + (n-1) d ). To solve, you simply substitute. .
T(n)=1 + ( n-1)3
T(n)=1 + 3n-3
T(n) =3-2n
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