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Write down first five terms of each sequence...
use what's given and substitute the number of the term in sequence into 'N'
when you see a^n-1....
What does recursive mean?
Recursive means to not use the number in sequence but the value of the first number in the sequence to give you the second number..
- for example:
- 1, 6, 9
- ...Use the 9 in place of n instead of using the 3 for the 3rd number in a sequence
Find the nth term of the sequence pattern given...
How do you solve these?
- 1st see if it is recurse or explicit
- If recurse you know that it should be set up
- an=a1 x (what each previous value is multilplied by) ^n-1
- If Explicit:
- See what n, the # in sequence is added to.. example:
- pretty much explain the pattern and how you would get an=FORMULA..give formula
Finding the sum of a sequence with greek symbol
- Top number= n, or number your trying to get to
- bottom number = what number of the sequence your starting with
- Middle number= formula used to find vaules...so the 'k' in these mini formulas you would put the sequence number (12345..)
- so you do that all the way until you get to the sequence number at top..then you add up all the vaules and that gives you the sum
Expressing the sum using summation notation..
aka: find the greek symbol looking thing for the pattern of numbers given..
- there will be a coulple numbers then a ....( Formula)
- in the formula the number in exponent will be the top number (aka the sequence number you stop at)
- The entire formula with be the middle formula but the # in the exponent will be replaced with a 'n' or 'k'...
- To find the bottom number you need to plug in the first sequence number..it the answer you get is equal to the first vaule given in the pattern, then your good. if higher or lower then the pattern given may be starting on sequence number 'o' or '2'...ect
is the common difference is being added or subtracted
multiplying by the same thing each time
Find the indicated term in each sequence..
- it will say for example:
- find the 8th term of this sequence..blah, blah, blah, blah
First find if Geometric or Arithmetic..
- If Arithmetic:
- Use the formula an= a1 + (n-1)d
plug in a8= first term + (8-1)(whatever the common difference is)
If Geometric use: An=a1 (r^n-1)
Double check ALWAYS... write the formula out to that value and try to get to it...
Combination vs Permutaion
- Combination: Order Not important
- Permutaion: Order very important
choices (c/p) spaces