70, 72, 77, 88, 105, ?
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The next term in 70, 72, 77, 88, 105, ? is 128
Solution:
The given series is 70, 72, 77, 88, 105, ?
Let the missing number be ‘x’
If we subtract the consecutive numbers we get,
72 – 70 = 2
77 – 72 = 5
88 – 77 = 11
105 – 88 =17
If we look closely we find that the difference between consecutive numbers of the given series are prime numbers.
2, 5, 11, 17
The prime numbers are 2,3,5,7,11,13,17,19,23.......
When we compare the prime numbers to the differences we can find that the required prime number to calculate the missing number ‘x’ in the series is 23.
Therefore, x = 105 + 23 =128.
Hence the next term is 128
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