# Find the next term of the series 7, 11, 23, 51, 103?

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

Answer

Verified

328.2k+ views

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.

Last updated date: 02nd Jun 2023

•

Total views: 328.2k

•

Views today: 5.84k

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?