Sequence & Series Level-2 Quiz-2

1. All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?

2. Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is?

3. a 1 = 1 and a n + 1 = 2 a n + 5 for n being a natural number. The value of a 100 is?

4. If a, b, c and d are four positive real numbers such that abcd = 1 , what is the minimum value of (1 + a) (1 + b) (1 + c) (1 + d)?

5. In a certain examination paper, there are n questions. For j = 1,2 ….n, there are 2^n–j students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is

6. Consider the set S = {1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

7.

8. If 1/(1^2) + 1/(2^2) + 1/(3^2)………..infinte = s. Find the value of 1/(1^2) – 1/(2^2) + 1/(3^2) – 1/(4^2)……infinite.

9. Find the sum of (1 + 2 + 3 + …n) + (2 + 3 + …n) + (3 + 4 + …n) + …+ (n).

10. The third term of an A.P. is 15 and the 23rd term is 55. Find the 40th term.