Discussion
Which of the following will complete the series ?
17, 23, 37, 53, ........ .
Answer: C
The next term is 73.
All the terms are primes. Counting primes in order (2, 3, 5, 7, 11, 13, 17, ...), 17 is the 7th prime, 23 the 9th, 37 the 12th and 53 the 16th. The positions go up by 2, 3 and 4, so the next step is 5, giving position 21. \[ 16 + 5 = 21 \] The 21st prime is 73.
The other options are primes too but sit at the wrong places: 59 is the 17th, 61 the 18th and 71 the 20th. That is why the series cannot be settled by the differences of the terms (6, 14, 16), which follow no simple rule.
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