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Find the missing number from the given responses. 3,10,20,33,49,68,?
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Find the missing number from the given responses. 3,10,20,33,49,68,?
Missing Number in the Sequence



  • Observing the Given Sequence: The given sequence of numbers is 3, 10, 20, 33, 49, 68, ?

  • Finding the Pattern: To find the missing number, we need to observe the pattern in the given sequence.

  • Calculating the Differences: The first differences between the consecutive terms are 7, 10, 13, 16, 19. We can observe that the second differences are constant and equal to 3. This indicates that the sequence follows a quadratic pattern.

  • Using the Quadratic Formula: We can use the quadratic formula to find the next term in the sequence. Let's assume that the nth term in the sequence is given by the quadratic formula: an = a + bn + cn^2. Then we can find the values of a, b, and c by using the first three terms of the sequence.

  • Calculating the Coefficients: Using the values of the first three terms, we get three equations:

    • a + b + c = 3

    • a + 2b + 4c = 10

    • a + 3b + 9c = 20


    Solving these equations, we get a = -1, b = 8, and c = 2.

  • Calculating the Missing Number: Now that we have the quadratic formula for the sequence, we can use it to calculate the missing term. Plugging in n = 7, we get a7 = -1 + 8(7) + 2(7)^2 = 99.

  • Answer: Therefore, the missing number in the sequence is 99.

Community Answer
Find the missing number from the given responses. 3,10,20,33,49,68,?
Missing Number in the Sequence


The given sequence is 3, 10, 20, 33, 49, 68, ?. We need to find the missing number in this sequence. Let's analyze the sequence to find out the pattern.


Analysis of the Sequence


On analyzing the sequence, we can observe the following:


  • The first number is 3.

  • The difference between the first and second number is 7 (10 - 3).

  • The difference between the second and third number is 10 (20 - 10).

  • The difference between the third and fourth number is 13 (33 - 20).

  • The difference between the fourth and fifth number is 16 (49 - 33).

  • The difference between the fifth and sixth number is 19 (68 - 49).



Therefore, we can see that the differences between the consecutive numbers in the sequence are increasing by 3. Based on this pattern, we can find the missing number in the sequence.


Finding the Missing Number


Using the pattern we identified, we can find the missing number in the sequence:


  • The difference between the sixth and the missing number is 22.

  • So, the missing number can be found by adding 22 to the last number in the sequence.

  • The last number in the sequence is 68.

  • Therefore, the missing number is 68+22=90.



Conclusion


Thus, the missing number in the sequence is 90.
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Find the missing number from the given responses. 3,10,20,33,49,68,?
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Find the missing number from the given responses. 3,10,20,33,49,68,? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the missing number from the given responses. 3,10,20,33,49,68,? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the missing number from the given responses. 3,10,20,33,49,68,?.
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