The answer is given in the following sentence.
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The next number is the sequence is 10. To find the second number, 1 was subtracted from the first number To find the third number, 2 was subtracted from the second number To find the fourth number, 3 was subtracted from the third number Therefore to find the fifth number, 4 must be subtracted from the fourth number. 14 - 4 = 10
To find two numbers that add to 20 and multiply to 29, we can set up a system of equations. Let's call the two numbers x and y. We have the following equations: x + y = 20 and x * y = 29. By solving these equations simultaneously, we find that the two numbers are 5 and 15.
The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.
They are equations that involve many steps to find the solution.
The following is the answer.
we can cross multiply the two equivalent equations and then find the fourth proportional
If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.
If the Fibonacci sequence is denoted by F(n), where n is the first term in the sequence then the following equation obtains for n = 0.
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A single number, such as 13579, does not define a sequence.
The next number is the sequence is 10. To find the second number, 1 was subtracted from the first number To find the third number, 2 was subtracted from the second number To find the fourth number, 3 was subtracted from the third number Therefore to find the fifth number, 4 must be subtracted from the fourth number. 14 - 4 = 10
A recursive sequence uses previous numbers to find the next number in a sequence after the base case. The Fibonacci sequence is an example of such a sequence. The base numbers of the Fibonacci sequence are 0 and 1. After that base, you find the next number in the sequence by adding the two previous numbers. So, the Fibonacci sequence looks like so: 0, 1, 1, 2, 3, 5, 8.... So, the third number is found by adding the first and second numbers, 0 and 1. So the third number is 1. The fourth number is found by adding the second and third numbers, 1 and 1. So, the fourth number is 2. You can continue on this way forever.
To effectively solve recurrence equations, one can use techniques such as substitution, iteration, and generating functions. These methods help find a closed-form solution for the recurrence relation, allowing for the calculation of specific terms in the sequence.
In a circle, the circumference and diameter vary directly. Which of the following equations would allow you to find the diameter of a circle with a circumference of 154 if you know that in a second circle the diameter is 14 when the circumference is 44?
To find two numbers that add to 20 and multiply to 29, we can set up a system of equations. Let's call the two numbers x and y. We have the following equations: x + y = 20 and x * y = 29. By solving these equations simultaneously, we find that the two numbers are 5 and 15.
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.