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An ordered list of numbers is called a sequence, and each individual number is a term. Here is a simple sequence of consecutive even integers.
2, 4, 6, 8, 10.…
Here you may assume the next number of the sequence is 12, but often you can't make these assumptions.
Sequence Formula
Sequences use "subscript" which is small font at the foot of a letter.
Think of this as a mechanism that generates integer numbers and runs them through a function like a computer.
an = 5 + n
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Here the subscript n is defined by the rule 5 + n. So this sequence will be a series of multiples of integers + 5 starting with 1.
5, 6, 7, 8, 9, 10, 11, 12..... |
an = 5n
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Here the subscript n is defined by the rule 5n. So this sequence will be a series of multiples of 5:
5, 10, 15, 20, 25, 30.... |
The key to solving these problems is to determine the relationship between the terms in the sequence that you are given. This relationship can be described in terms of a progression, a function or manipulation that can be applied to each individual term of a sequence that will generate the next term in that sequence.
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Trick Question Alert
Mr. GMAT likes to fool you by making a list of numbers like
3, 5, 7, _
Guess what is next in this sequence?
No, it is not 9, it is 11. You thought it was consecutive odd numbers, but it was actually consecutive primes. On Data Sufficiency questions, be keenly aware of the limitations when calculating sequences. |
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Arithmetic Progressions
Progressions where there is a constant distance between each term.
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