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.
-7
In this case, 22 would have the value of 11.
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.
12, 6, 0, -6, ...
It look like a Fibonacci sequence seeded by t1 = 2 and t2 = 1. After that the recursive formula is simply tn+1 = tn-1 + tn.
what is the recursive formula for this geometric sequence?
4, -1236, -108 is not a geometric system.
-7
In this case, 22 would have the value of 11.
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.
The common difference between recursive and explicit arithmetic equations lies in their formulation. A recursive equation defines each term based on the previous term(s), establishing a relationship that builds upon prior values. In contrast, an explicit equation provides a direct formula to calculate any term in the sequence without referencing previous terms. While both methods describe the same arithmetic sequence, they approach it from different perspectives.
by the general formula ,a+(n-1)*d * * * * * That assumes that it is an arithmetic sequence. The sequence cound by geometric ( t(n) = a*rn ) or power ( t(n) = n2 ) or something else.
There are different answers depending upon whether the sequence is an arithmetic progression, a geometric progression, or some other sequence. For example, the sequence 4/1 - 4/3 + 4/5 - 4/7 adds to pi
because starwars is awesome
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
12, 6, 0, -6, ...