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Find the missing term in the sequence: 10, 14, 26, 42, 70, ?

Mathematics

ScanSolve AI Answer

Answer

114

Step-by-step solution

4 steps
  1. Find the differences between consecutive terms in the given sequence.

    The sequence is 10,14,26,42,70,?10, 14, 26, 42, 70, ?
    Calculate the first differences:

    14−10=414 - 10 = 4 26−14=1226 - 14 = 12 42−26=1642 - 26 = 16 70−42=2870 - 42 = 28

    The sequence of differences is 4,12,16,284, 12, 16, 28.

  2. Identify the pattern in the sequence of differences.

    Let's examine if there's a relationship between these differences.
    Notice that:

    16=12+416 = 12 + 4 28=16+1228 = 16 + 12

    This shows that each difference (starting from the third one) is the sum of the two preceding differences. This is a Fibonacci-like sequence for the differences.

  3. Apply the pattern to find the next difference.

    Following this pattern, the next difference will be the sum of the last two differences found:
    Next difference =28+16=44= 28 + 16 = 44.

  4. Add the next difference to the last term of the original sequence to find the missing term.

    The last term in the given sequence is 70.
    Missing term =70+44=114= 70 + 44 = 114.

    The complete sequence is 10,14,26,42,70,11410, 14, 26, 42, 70, 114.

    The missing term is 114.

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