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Question

Answers

A) 186 B) 188 C) 185 D) 187 E) none of the above

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Hint: To solve this problem we should do basic math, logical thinking .This problem can be solved by finding out the pattern of the series.

Complete step-by-step answer:

The given series is 7, 11, 23, 51, 103,

We know that every series has a pattern that means the given series also has a pattern.

So let us find out the pattern of the given series.

Here the pattern of series is

$7 + 4 \times 1 = 11$

$11 + 4 \times 3 = 23$

$23 + 4 \times 7 = 51$

$51 + 4 \times 13 = 103$

$103 + 4\times 21 = 187$

If we observe the pattern given we have taken first term of series and added 4 and multiplied 1 to the first term which gave us the second term of series, to get the third term we have applied the same process in which the term we are adding is constant but the term we are multiplying has a difference of multiple of 2.So if we observe terms 1,3,7,13,21 has the difference of the form 2,4,6,8 and so on.

So, now on following the pattern we got the 6th term as 187.

Option D is the correct answer.

Note: To solve these kinds of problems we don’t need any theorems. It is simple logical thinking. For this kind of problem the first thing is to trace out the pattern of the series and apply it further to get the next term. Here we have to make a note that we have to check whether all the numbers in the series follow the pattern are not. If one term is not satisfying the pattern then we can that it is not the pattern of series.

Complete step-by-step answer:

The given series is 7, 11, 23, 51, 103,

We know that every series has a pattern that means the given series also has a pattern.

So let us find out the pattern of the given series.

Here the pattern of series is

$7 + 4 \times 1 = 11$

$11 + 4 \times 3 = 23$

$23 + 4 \times 7 = 51$

$51 + 4 \times 13 = 103$

$103 + 4\times 21 = 187$

If we observe the pattern given we have taken first term of series and added 4 and multiplied 1 to the first term which gave us the second term of series, to get the third term we have applied the same process in which the term we are adding is constant but the term we are multiplying has a difference of multiple of 2.So if we observe terms 1,3,7,13,21 has the difference of the form 2,4,6,8 and so on.

So, now on following the pattern we got the 6th term as 187.

Option D is the correct answer.

Note: To solve these kinds of problems we don’t need any theorems. It is simple logical thinking. For this kind of problem the first thing is to trace out the pattern of the series and apply it further to get the next term. Here we have to make a note that we have to check whether all the numbers in the series follow the pattern are not. If one term is not satisfying the pattern then we can that it is not the pattern of series.