NCERT Solutions Ganita Prakash (Part 1) Chapter 6 .4 This Way or That Way, All Ways Lead to the Bay — In-text Questions
Book page 1506 Updated on2026-09-05
Q1.
Observe the pattern in the figure below. Draw the next figure in the sequence. How many circles does it have? How many total circles are there in Step 10? Write an expression for the number of circles in Step k.
Answer
Counting the printed figures: Step 1 has 3 circles, Step 2 has 8, Step 3 has 15.
The next figure (Step 4) is a 5 by 5 block of circles with one corner circle missing — 24 circles.
Step 4: a 5 × 5 square of circles with the corner one missing — 25 – 1 = 24 circles.
Expression for Step k. Each figure is a (k + 1) by (k + 1) square with one circle removed:
Step k = (k + 1)² – 1 = k² + 2k + 1 – 1 = k² + 2k
Step k
1
2
3
4
10
k² + 2k
3
8
15
24
120
Step 10 has 10² + 2 × 10 = 120 circles.
Why it happens: the figure grows by adding one row and one column each time, so its “full square” side goes 2, 3, 4, 5, … — that is k + 1 at Step k — and exactly one circle is always missing from the corner.