Admission

1. Can you recognise the pattern in each of the sequences in Table 1? Ans: (a) 1, 1, 1, 1, 1, 1, 1, …… The number ‘1’ is repeated indefinitely. (b) 1, 2, 3, 4, 5, 6, 7, …… Counting numbers starting from ‘1’. Each number increases by 1. (c) 1, 3, 5, 7, 9, 11, 13, …… Odd numbers. Start from 1 and keep adding 2. (d) 2, 4, 6, 8, 10, 12, 14, …… Even numbers. Start from 2 and keep adding 2. (e) 1, 3, 6, 10, 15, 21, 28, …… Triangular numbers. Each term is the sum of the natural numbers up to that term. (f) 1, 4, 9, 16, 25, 36, 49, …… Square numbers. Each term is the square of its position (12, 22, 32, ...). (g) 1, 8, 27, 64, 125, 216, …… Cube numbers. Each term is the cube of its position ((12, 22, 32, ...). (h) 1, 2, 3, 5, 8, 13, 21, …… Virahānka numbers (Fibonacci sequence). Each number is the sum of the two preceding numbers. (i) 1, 2, 4, 8, 16, 32, 64, …… Powers of 2. Each term is raised to the power of its position (20, 21, 22, ...). (j) 1, 3, 9, 27, 81, 243, 729, …… Powers of 3. Each te...