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arithmetic sequence
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A recursive formula can produce arithmetic, geometric or other sequences.
For example, for n = 1, 2, 3, ...:
u0 = 2, un = un-1 + 5 is an arithmetic sequence.
u0 = 2, un = un-1 * 5 is a geometric sequence.
u0 = 0, un = un-1 + n is the sequence of triangular numbers.
u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares.
u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
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What recursive formulas represents the same arithmetic sequence as the explicit formula an 5 n - 12?
-7
Can a sequence of numbers be both geometric and arithmetic?
Yes, it can both arithmetic and geometric.The formula for an arithmetic sequence is: a(n)=a(1)+d(n-1)The formula for a geometric sequence is: a(n)=a(1)*r^(n-1)Now, when d is zero and r is one, a sequence is both geometric and arithmetic. This is because it becomes a(n)=a(1)1 =a(1). Note that a(n) is often written anIt can easily observed that this makes the sequence a constant.Example:a(1)=a(2)=(i) for i= 3,4,5...if a(1)=3 then for a geometric sequence a(n)=3+0(n-1)=3,3,3,3,3,3,3and the geometric sequence a(n)=3r0 =3 also so the sequence is 3,3,3,3...In fact, we could do this for any constant sequence such as 1,1,1,1,1,1,1...or e,e,e,e,e,e,e,e...In general, let k be a constant, the sequence an =a1 (r)1 (n-1)(0) with a1 =kis the constant sequence k, k, k,... and is both geometric and arithmetic.
A certain arithmetic sequence has the recursive formula If the common difference between the terms of the sequence is -11 what term follows the term that has the value 11?
In this case, 22 would have the value of 11.
What is the formula for the following arithmetic sequence?
12, 6, 0, -6, ...
What is the difference between arithmetic mean and geometric mean?
Arhithmetic progression is linear, while geometric grows in a parabolic way (a curve).
