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Question: Complete the following series: \[2,3,6,10,17,28,?\] A). \[45\] B). \[46\] C). \[35\] D). \[4...

Complete the following series: 2,3,6,10,17,28,?2,3,6,10,17,28,?
A). 4545
B). 4646
C). 3535
D). 4040

Explanation

Solution

In such types of questions, first we find the relation between the given terms in the series and then find the subsequent terms to reach the desired answer. This relation could be anything but the mathematical relation either be it any addition, subtraction, any multiplication, division, or any other mathematical function.

Complete step-by-step solution:
2,3,6,10,17,28,?2,3,6,10,17,28,?
To find the relation between the given terms of the series, find the difference between all the terms.
The difference between first two terms of the series i.e., 2&32\& 3 is:
3−2=13 - 2 = 1
The difference between second and third term of the series is:
6−3=36 - 3 = 3
The difference between third and fourth term of the series is:
10−6=410 - 6 = 4
The difference between fourth and fifth term of the series is:
17−10=717 - 10 = 7
The difference between fifth and sixth term is:
28−17=1128 - 17 = 11
Now, we will make the series of all the differences we got,
1,3,4,7,11,.....1,3,4,7,11,.....
By observing the above series, we get to know that it is a Fibonacci series, in which we obtain a term by adding previous two terms
So the next term in the obtained Fibonacci series will be obtained by adding last two numbers of the series,
11+7=1811 + 7 = 18
It implies that 1818 is the difference between the sixth term and the required term of the given series.
Hence the required term of the series will be
28+18=4628 + 18 = 46
Final Answer: The next term of this series will be (B). 4646.

Note: The Fibonacci sequence is a series of numbers in which each number is the addition of the two previous terms, which is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,….0,{\text{ }}1,{\text{ }}1,{\text{ }}2,{\text{ }}3,{\text{ }}5,{\text{ }}8,{\text{ }}13,{\text{ }}21,{\text{ }}34,{\text{ }}55, \ldots .. Therefore, 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 30{\text{ }} + {\text{ }}1{\text{ }} = {\text{ }}1,{\text{ }}1{\text{ }} + {\text{ }}1{\text{ }} = {\text{ }}2,{\text{ }}1{\text{ }} + {\text{ }}2{\text{ }} = {\text{ }}3 and so on. The Fibonacci sequence is important because of the golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the previous term, except for the first few numbers.