A few of the things we learned to do in this lesson are:
1. Find terms of a sequence.
2. Write equations of sequences.
3. Evaluate factorials.
1. Sequences are often represented as an equation like an = 2n - 1. To find a specific term, like the third term (a3), plug the number of the term into the equation as n. 2(3) - 1 = 5.
2. Finding the equation of a sequence can be tricky, but the best method is to just list the sequence with the number of each term under it., like so: sequence: 1 3 5 7
n: 1 2 3 4
The pattern can be determined from there.
3. A factorial (!) is a product of consecutive natural numbers, leading up to the number by which the product is represented.
For example, 5! = 5x4x3x2x1.
A lot of times equations that involve factorials can appear overwhelming at first, but simplification is possible if there is division involved:
Example: 100!/99! -----> The denominator cancels out the first 99 factors of the product 100!, so the only number left is 100. Therefore, the answer is 100.
Most of these problems involve a lot of logical thinking rather than plug-and-chug equations. This is good for some students who understand that logic, but it can be a struggle for other students.
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