NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Exploring linear patterns
Book page 22 Updated on2026-09-08
Q1.
Predict the number of squares in the next three stages of the pattern and write the sequence of numbers up to Stage 7 of the pattern.
Answer
Stages 1 to 4 of Fig. 2.4 use 1, 3, 5 and 7 tiles. Each new stage adds two tiles — one to each column — so the next three stages use 9, 11 and 13 tiles.
Stage
1
2
3
4
5
6
7
Number of square tiles
1
3
5
7
9
11
13
Sequence up to Stage 7: 1, 3, 5, 7, 9, 11, 13.
Stages 5, 6 and 7 drawn out: each is a two-wide column with one extra tile on top, so the growth is exactly 2 tiles a stage.
Why exactly two each time: look at the shape, not only at the numbers. Stage n is a block two tiles wide and (n − 1) tiles tall, with a single tile perched on top of the right column. Moving to the next stage raises the block by one row — that is 2 tiles — and the lone tile on top just moves up with it. The count is therefore 2(n − 1) + 1 = 2n − 1, and the constant difference 2 is the coefficient of n.
Tip: Predicting from the picture and from the rule should agree. 2(7) − 1 = 13, which matches the drawing of Stage 7.