Answer
Verified
456.9k+ views
Hint: We start solving by calculating the difference between every two consecutive numbers of the sequence. Once we calculate the differences, we can see that these differences are in AP (Arithmetic Progression). Using this AP (Arithmetic Progression), we find the difference 31 and the next number in the sequence. Once we find the difference, we add it to 31 to get the next number in the sequence.
Complete step-by-step solution:
We have a sequence given in the problem as 1, 5, 10, 16, 23, 31……. We need to find the next number which is missing in the sequence.
We need to find the logic that is present between all these numbers. Let us find the difference between the consecutive numbers present in the sequence.
Now, we find the difference between 1 and 5 and let it be ${{d}_{1}}$.
So, we have \[{{d}_{1}}=5-1\].
We have ${{d}_{1}}=4$ ----------(1).
Now, we find the difference between 5 and 10 and let it be ${{d}_{2}}$.
So, we have \[{{d}_{2}}=10-5\].
We have ${{d}_{2}}=5$ -----------(2).
Now, we find the difference between 10 and 16 and let it be ${{d}_{3}}$.
So, we have \[{{d}_{3}}=16-10\].
We have ${{d}_{3}}=6$ ----------(3).
Now, we find the difference between 16 and 23 and let it be ${{d}_{4}}$.
So, we have \[{{d}_{4}}=23-16\].
We have ${{d}_{4}}=7$ ----------(4).
Now, we find the difference between 23 and 31 and let it be ${{d}_{5}}$.
So, we have \[{{d}_{5}}=31-23\].
We have ${{d}_{5}}=8$ ----------(5).
From equations (1), (2), (3), (4) and (5), we can see that ${{d}_{1}}$, ${{d}_{2}}$, ${{d}_{3}}$, ${{d}_{4}}$ and ${{d}_{5}}$ are A.P (Arithmetic Progression) with a common difference of 1.
Let us assume that the next number in the sequence be ‘x’ and the difference between ‘x’ and 31 be ${{d}_{6}}$.
We can find ${{d}_{6}}$ by adding 1 to ${{d}_{5}}$.
So, ${{d}_{6}}=1+{{d}_{5}}$.
${{d}_{6}}=1+8$.
${{d}_{6}}=9$.
Now, the value of ‘x’ is $x=31+{{d}_{6}}$.
$x=31+9$.
$x=40$.
$\therefore$ The next number in the sequence is 40.
The correct option for the given problem is (d).
Note: We always need to check whether we get any relation between the differences of two consecutive terms of the sequence. We should not make any calculation errors while calculating the difference and next numbers. Similarly, we can expect to find the next three terms of sequence, the sum of the next three terms in the sequence, the product of the next three terms in the sequence.
Complete step-by-step solution:
We have a sequence given in the problem as 1, 5, 10, 16, 23, 31……. We need to find the next number which is missing in the sequence.
We need to find the logic that is present between all these numbers. Let us find the difference between the consecutive numbers present in the sequence.
Now, we find the difference between 1 and 5 and let it be ${{d}_{1}}$.
So, we have \[{{d}_{1}}=5-1\].
We have ${{d}_{1}}=4$ ----------(1).
Now, we find the difference between 5 and 10 and let it be ${{d}_{2}}$.
So, we have \[{{d}_{2}}=10-5\].
We have ${{d}_{2}}=5$ -----------(2).
Now, we find the difference between 10 and 16 and let it be ${{d}_{3}}$.
So, we have \[{{d}_{3}}=16-10\].
We have ${{d}_{3}}=6$ ----------(3).
Now, we find the difference between 16 and 23 and let it be ${{d}_{4}}$.
So, we have \[{{d}_{4}}=23-16\].
We have ${{d}_{4}}=7$ ----------(4).
Now, we find the difference between 23 and 31 and let it be ${{d}_{5}}$.
So, we have \[{{d}_{5}}=31-23\].
We have ${{d}_{5}}=8$ ----------(5).
From equations (1), (2), (3), (4) and (5), we can see that ${{d}_{1}}$, ${{d}_{2}}$, ${{d}_{3}}$, ${{d}_{4}}$ and ${{d}_{5}}$ are A.P (Arithmetic Progression) with a common difference of 1.
Let us assume that the next number in the sequence be ‘x’ and the difference between ‘x’ and 31 be ${{d}_{6}}$.
We can find ${{d}_{6}}$ by adding 1 to ${{d}_{5}}$.
So, ${{d}_{6}}=1+{{d}_{5}}$.
${{d}_{6}}=1+8$.
${{d}_{6}}=9$.
Now, the value of ‘x’ is $x=31+{{d}_{6}}$.
$x=31+9$.
$x=40$.
$\therefore$ The next number in the sequence is 40.
The correct option for the given problem is (d).
Note: We always need to check whether we get any relation between the differences of two consecutive terms of the sequence. We should not make any calculation errors while calculating the difference and next numbers. Similarly, we can expect to find the next three terms of sequence, the sum of the next three terms in the sequence, the product of the next three terms in the sequence.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE