RAS question
Find the next number in the series: 2, 5, 10, 17, 26, ?
Correct answer: (C) 37.
The next number in the series 2, 5, 10, 17, 26 is 37, because the terms follow n squared plus 1 for n = 1 to 6.
Explanation
The series can be read in two consistent ways. First, the consecutive differences are 3, 5, 7 and 9; these are increasing odd numbers, so the next difference is 11 and 26 + 11 = 37. Second, each term is one more than a square: 1 squared + 1 = 2, 2 squared + 1 = 5, 3 squared + 1 = 10, 4 squared + 1 = 17 and 5 squared + 1 = 26, so the next term is 6 squared + 1 = 37. NCERT treats number sequences and square numbers as basic mathematical patterns, and also notes the close relation between adding odd numbers and forming squares.
Why the other options are wrong
- (A) 35 would add 9 again to 26, but the difference pattern has already used 9 and must move to the next odd difference, 11.
- (B) 36 is 6 squared, but the established formula is n squared plus 1, so the sixth term must be 37, not 36.
- (D) 38 would require adding 12 to 26, which breaks the odd-difference sequence 3, 5, 7, 9, 11.
Concept
This tests number-series pattern recognition, especially differences and square-number forms. It recurs in RAS reasoning because such questions reward spotting a compact rule rather than doing lengthy calculation.