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1 1 , 2 2 , 4 4 , 8 8 , 16 16. This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 2 gives the next term. In other words, an = a1rn−1 a n = a 1 r n - 1. Geometric Sequence: r = 2 r = 2. This is the form of a geometric sequence.
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11 Φεβ 2017 · Explanation: We have a sequence of numbers: 1,2,4,8,16,... Is it arithmetic? An arithmetic sequence will have the same difference between any two consecutive numbers. Let's see if we have that here: ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝ higher consecutive lower consecutive difference 2 1 1 4 2 2 8 4 4 ⋮ ⋮ ⋮ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠. And so no - this is not arithmetic.
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A geometric progression (GP), also called a geometric sequence, is a sequence of numbers which differ from each other by a common ratio. For example, the sequence 2, 4, 8, 16, \dots 2,4,8,16,… is a geometric sequence with common ratio 2 2. We can find the common ratio of a GP by finding the ratio between any two adjacent terms.
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If we start indexing at $n = 1$, we get $$a_n = 2^{\lceil \log_2 n\rceil}$$where $\lceil - \rceil$ is the ceiling function.
