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Lostsunrise [7]
3 years ago
6

In the following sequence, each number (except the first two) is the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, .

... This sequence is known as the Fibonacci sequence. We speak of the i'th element of the sequence (starting at 0)-- thus the 0th element is 0, the 1st element is 1, the 2nd element is 1, the 3rd element is 2 and so on. Given the positive integer n, associate the nth value of the fibonacci sequence with the variable result. For example, if n is associated with the value 8 then result would be associated with 21.

Mathematics
1 answer:
Amanda [17]3 years ago
8 0

Answer:

Fibonacci Series has been explained and the general term and shortcut to find the corresponding term has been attached

Step-by-step explanation:

Fibonnaci is a beautiful series in mathematics where the term in the series is the sum of the previous two terms of the corresponding term in the series.

Its general form is denoted by

X_{n} =X_{n-1}+X_{n-2},

where X_{n} represents the n^{th} of the Fibonnaci series.

The special thing about the Fibonacci series is that the more number of terms we proceed the ratio of the two consecutive term comes closer to the value of the Golden Ratio(φ) whose value is 1.618034.

But there is another method to find out the terms of the the Fibonacci series, which takes into account the value of φ. The formula for the following is as follows

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How many integers from 1 through 100 are neither multiples of 2 nor multiples of 3 ?
julia-pushkina [17]
----------------------------------------------------------------------------
Find total number of integers
----------------------------------------------------------------------------
Number of integers from 1 to 100 = 100
There are 100 numbers altogether

----------------------------------------------------------------------------
Find total numbers that can be divided by 2
----------------------------------------------------------------------------
Number that are multiples of 2 = 100 ÷ 2 = 50
50 of the number are multiples of  2

----------------------------------------------------------------------------
Find total numbers that are multiples of 3
----------------------------------------------------------------------------
Numbers that are multiples of 3 = 100 ÷ 3 = 33 R 1
33 of the numbers are multiples of 3

Of the 33 numbers that are multiples of 3, half of the numbers are even and had been included in multiples of 2.
33 ÷ 2 = 16 R 1

33 - 16 = 17
17 of the numbers are multiples of 3

----------------------------------------------------------------------------
Total numbers that can be multiples of 2 or 3
----------------------------------------------------------------------------
50 + 17 = 67

----------------------------------------------------------------------------
Total number that are neither multiples of 2 nor 3
----------------------------------------------------------------------------
100 - 67 = 33

----------------------------------------------------------------------------
Ans: 33 integers are neither multiples of 2 nor multiples  3
----------------------------------------------------------------------------
8 0
3 years ago
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