Class 6 NCERT Maths chapter 1 solution 2025

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 term is 3 raised to the power of its position (30, 31, 32, ...).

This is a sequence of consecutive counting numbers. The next three numbers are 8, 9, and 10.

(c) 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, …

These are consecutive odd numbers, increasing by 2. The next three numbers are 15, 17, and 19.

(d) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

The sequence contains even numbers, increasing by 2. The next three numbers are 16, 18, and 20.

(e) 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

A sequence of triangular numbers where each number is the sum of the natural numbers up to a certain point.
28 + 8 = 36
36 + 9 = 45
45 + 10 = 55

(f) 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …

Square numbers are formed by multiplying a number by itself. The next three are 64, 81, and 100.
82 = 64
92 = 81
102 = 100

(g) 1, 8, 27, 64, 125, 216, 343, 512, 729, …

A sequence of cube numbers where each number is the cube of a natural number. The next three numbers are 343, 512, and 729.
73 = 343
83 = 512
93 = 729

(h) 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

This is the Fibonacci (Virahanka) sequence, where each number is the sum of the previous two. The next three numbers are 34, 55, and 89.
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89

(i) 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, …

This shows powers of 2, where each number is multiplied by 2. The next three numbers are 128, 256, and 512.
64 × 2 = 128
128 × 2 = 256
256 × 2 = 512

(j) 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, …

This shows powers of 3, where each number is multiplied by 3. The next three numbers are 2187, 6561, and 19683.

729 × 3 = 2187

2187 × 3 = 6561

6561 × 3 = 19683