NCERT Solutions for Class 7th Maths Chapter 7 Matchstick Pattern — In-text Questions
Book page 166 – 167 Updated on2026-09-19
Q1.
Jasmine decides to make a matchstick arrangement that appears in this sequence, using exactly 99 sticks. What will be the position number of this arrangement in the sequence?The first four arrangements in the matchstick sequence, with their position numbers.
Answer
Position 49.
First find the rule for the number of sticks. Look at the arrangements one by one.
Position 1 has 2 × (1) + 1 = 3 matchsticks
Position 2 has 2 × (2) + 1 = 5 matchsticks
Position 3 has 2 × (3) + 1 = 7 matchsticks
So position n has 2n + 1 matchsticks
Now Jasmine wants 99 sticks, so we need the value of n for which 2n + 1 is 99.
2n + 1 = 99
2n = 99 − 1 = 98
n = 98 ÷ 2 = 49
Why it happens: the first triangle uses 3 sticks and every new triangle after that adds 2 more (the new triangle shares one stick with the one before it). So the count is "1 stick to start, then 2 for each triangle" — which is 2n + 1. Writing 2n + 1 = 99 turns Jasmine's question into a one-line equation.
Check it yourself: 2 × 49 + 1 = 98 + 1 = 99. ✓
Q2.
Can you find ways to get the value of n, such that 2n + 1 = 99?
Answer
Yes — here are three different ways, and all three give n = 49.
Undo the steps. The expression 2n + 1 was built by doubling n and then adding 1. Undo it in the reverse order: from 99 subtract 1 to get 98, then halve 98 to get 49.
Same operation on both sides. Subtract 1 from both sides: 2n + 1 − 1 = 99 − 1, so 2n = 98. Now divide both sides by 2: n = 98 ÷ 2 = 49.
Trial and error. Try n = 40 → LHS = 81, too small. Try n = 50 → LHS = 101, a bit too big. Try n = 49 → LHS = 99. Correct.
Why it happens: 2n + 1 grows steadily as n grows — every time n goes up by 1, the LHS goes up by 2. So the LHS passes 99 exactly once, and there is only one value of n that works. That is why all three methods must land on the same answer.
Tip: trial and error is fine for small numbers, but here you might have tested a dozen values. The second method reaches the answer in two lines, and it works just as fast for 2n + 1 = 9999.
Q3.
Is it possible to make a matchstick arrangement that appears in this sequence using exactly 200 sticks?
Page 166 — the first four matchstick arrangements in the sequence, with their position numbers.
Answer
No, it is not possible.
We would need 2n + 1 = 200
2n = 200 − 1 = 199
n = 199 ÷ 2 = 99.5
A position number must be a whole number — there is no 99.5th arrangement. So no arrangement in this sequence uses exactly 200 sticks.
Why it happens: 2n is always even, so 2n + 1 is always odd. Every arrangement in this sequence uses an odd number of sticks: 3, 5, 7, 9, 11, … . 200 is even, so it can never appear in that list. The arrangements jump from 199 sticks (position 99) straight to 201 sticks (position 100).
Check it yourself: position 99 needs 2 × 99 + 1 = 199 sticks and position 100 needs 201. There is no way to stop at 200.