It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
The sequence you've provided seems to be 3, 1, -1, -3, -5. To find the explicit formula for this sequence, we can observe that it starts at 3 and decreases by 2 for each subsequent term. The explicit formula can be expressed as ( a_n = 3 - 2(n-1) ) for ( n \geq 1 ). Simplifying this gives ( a_n = 5 - 2n ).
The given sequence can be identified as a geometric sequence where each term is multiplied by a common ratio. To find the explicit formula, we note that each term can be expressed as ( a_n = 3 \times (1.5)^{n-1} ), where ( n ) is the term number starting from 1. Thus, the explicit formula for the sequence is ( a_n = 3 \times (1.5)^{n-1} ).
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shemel mercurius
To find the 400th term of the sequence, we first identify the first term ( a_1 = 8 ) and the common difference ( d = 20 - 8 = 12 ). Using the explicit formula ( a_n = a_1 + (n - 1) \cdot d ), we can substitute ( n = 400 ): [ a_{400} = 8 + (400 - 1) \cdot 12 = 8 + 399 \cdot 12 = 8 + 4788 = 4796. ] Thus, the 400th term is 4796.
An explicit equation defines a sequence by providing a direct formula to calculate the nth term without needing the previous terms, such as ( a_n = 2n + 3 ). In contrast, a recursive equation defines a sequence by specifying the first term and providing a rule to find subsequent terms based on previous ones, such as ( a_n = a_{n-1} + 5 ) with an initial condition. Essentially, explicit equations allow for direct access to any term, while recursive equations depend on prior terms for computation.
write a java program to find factorial using recursive and non recursive
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The explicit formula here is 5+ 6x. solved at x=25 you get 155
The explicit formula for a sequence is a formula that allows you to find the nth term of the sequence directly without having to find all the preceding terms. To find the explicit formula for a sequence, you need to identify the pattern or rule that governs the sequence. This can involve looking at the differences between consecutive terms, the ratios of consecutive terms, or any other mathematical relationship that exists within the sequence. Once you have identified the pattern, you can use it to create a formula that will generate any term in the sequence based on its position (n) in the sequence.
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If you cannot find any iterative algorithm for the problem, you have to settle for a recursive one.
The sequence you've provided seems to be 3, 1, -1, -3, -5. To find the explicit formula for this sequence, we can observe that it starts at 3 and decreases by 2 for each subsequent term. The explicit formula can be expressed as ( a_n = 3 - 2(n-1) ) for ( n \geq 1 ). Simplifying this gives ( a_n = 5 - 2n ).
A recursive pattern is a pattern that goes like this 2,4,6,8 and on. A pattern rule which is used to find the next term.
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shemel mercurius
To find the 400th term of the sequence, we first identify the first term ( a_1 = 8 ) and the common difference ( d = 20 - 8 = 12 ). Using the explicit formula ( a_n = a_1 + (n - 1) \cdot d ), we can substitute ( n = 400 ): [ a_{400} = 8 + (400 - 1) \cdot 12 = 8 + 399 \cdot 12 = 8 + 4788 = 4796. ] Thus, the 400th term is 4796.