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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.
What else can I help you with?
What recursive formulas represents the same arithmetic sequence as the explicit formula an 5 n - 12?
-7
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.
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.
What is the formula for the following arithmetic sequence?
12, 6, 0, -6, ...
What is the recursive formula for 2 1 3 4 7 11?
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 difference between a geometric sequence and a recursive formula?
what is the recursive formula for this geometric sequence?
What is the recursive formula for this geometric sequence 4-1236-108...?
4, -1236, -108 is not a geometric system.
What recursive formulas represents the same arithmetic sequence as the explicit formula an 5 n - 12?
-7
Is the explicit rule for a geometric sequence defined by a recursive formula of for which the first term is 23?
Yes, the explicit rule for a geometric sequence can be defined from a recursive formula. If the first term is 23 and the common ratio is ( r ), the explicit formula can be expressed as ( a_n = 23 \cdot r^{(n-1)} ), where ( a_n ) is the nth term of the sequence. This formula allows you to calculate any term in the sequence directly without referencing the previous term.
How do you work out the 20th term of a sequence?
To find the 20th term of a sequence, first identify the pattern or formula that defines the sequence. This could be an arithmetic sequence, where each term increases by a constant difference, or a geometric sequence, where each term is multiplied by a constant factor. Once the formula is established, substitute 20 into the formula to calculate the 20th term. If the sequence is defined recursively, apply the recursive relation to compute the 20th term based on the previous terms.
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.
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.
What is the common difference between recursive and explicit arithmetic equations?
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.
What are recursive formulas for the nth term geometric sequence?
A recursive formula for the nth term of a geometric sequence defines each term based on the previous term. It can be expressed as ( a_n = r \cdot a_{n-1} ), where ( a_n ) is the nth term, ( a_{n-1} ) is the previous term, and ( r ) is the common ratio. Additionally, you need an initial term ( a_1 ) to start the sequence, such as ( a_1 = a ), where ( a ) is the first term.
How do you find out the nth term?
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.
What is the formula for sequence sum?
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
What is the formula for non arithmetic and geometric sequences?
because starwars is awesome
