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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.
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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.
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
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.
What is the form of a sequence where you get one term by doing something to the previous term?
Recursive Form
What is A sequence or series in which the value of a term depends on the previous term?
A sequence or series in which the value of a term depends on the previous term is known as a recursive sequence. In such sequences, each term is defined in relation to one or more of its predecessors, often utilizing a specific formula or rule. Common examples include the Fibonacci sequence, where each term is the sum of the two preceding terms, and arithmetic or geometric sequences, where each term is generated by adding or multiplying a constant to the previous term.
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.
What is the difference between an arithmetic sequence and a geometric sequence?
In an arithmetic sequence the same number (positive or negative) is added to each term to get to the next term.In a geometric sequence the same number (positive or negative) is multiplied into each term to get to the next term.A geometric sequence uses multiplicative and divisive formulas while an arithmetic uses additive and subtractive formulas.
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
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.
What is the form of a sequence where you get one term by doing something to the previous term?
Recursive Form
What is A sequence or series in which the value of a term depends on the previous term?
A sequence or series in which the value of a term depends on the previous term is known as a recursive sequence. In such sequences, each term is defined in relation to one or more of its predecessors, often utilizing a specific formula or rule. Common examples include the Fibonacci sequence, where each term is the sum of the two preceding terms, and arithmetic or geometric sequences, where each term is generated by adding or multiplying a constant to the previous term.
What is the nth term of the geometric sequence 4 8 16 32 ...?
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
In the geometric sequence 4,12,36,....which term is 8748?
2946
How is the value of any term calculated if the position of term is known?
A sequence usually has a position-to-value function. Alternatively, it can be derived from the recursive relationship that defines the sequence.
When In a geometric sequence the term an plus 1 can be smaller than the term a?
Yes, it can.
What is the next term in the geometric sequence 4-1236?
1240
How do you determine if a sequence is geometric?
A sequence is geometric if each term is found by mutiplying the previous term by a certain number (known as the common ratio). 2,4,8,16, --> here the common ratio is 2.
