## nth Term of Special series - Advance

For example, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2. If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence ( ) is given by: , and in general .

Q1.  The number 111.......1 (91 times) is a

•  Even number
•   Prime number
•  Not prime
•   None of these

Not prime

Q2. The difference between an integer and its cube is divisible by

•  4
•  6
•  9
•  None of these

6

Q3.  In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8,......, where n consecutive terms have the value n , the 1025th term is

•   29
•  210
•  211
•   212

210

Q4.  Observe that 13=1 , 23 = 3 + 5 , 33 = 7 + 9 + 11 , 43 = 13 + 15 + 17 + 19 . Then n3 as a similar series is

•  (2n2 - n + 1) + (2n2 - n + 3) + (2n2 - n + 5) + ........... + (n2 - n + 1)
•   (n2 + n - 1) + (n2 + n - 3) + (n2 + n - 5) + ........... + (n2 + n - 1)
•  (n2 - n + 1) + (n2 - n + 3) + (n2 - n + 5) + ........... + (n2 - n + 1)
•  None of these

(n2 - n + 1) + (n2 - n + 3) + (n2 - n + 5) + ........... + (n2 - n + 1)

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