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NCERT Solutions for Class 9th Maths Chapter 8 In-text Questions — Introduction to Sequences

Book page 174–175 Updated on2026-09-08

Q1.
Can you think of other finite sequences that you see in your daily life?
Answer

Yes — a finite sequence is any ordered list that stops, and everyday life is full of them.

  • The overs bowled in a T20 innings: 1, 2, 3, …, 20.
  • The Indian currency notes in circulation: 10, 20, 50, 100, 200, 500.
  • The marks of a student in six subjects, written in the order of the report card.
  • The number of days in the twelve months of 2026: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31.
  • The stairs of a flight numbered from bottom to top, or the platform numbers at a railway station.
Why it happens: two conditions make a list a sequence — the items must be in a definite order, and each item must have a position number. A jumble of prices in a shop is not a sequence; the same prices arranged from cheapest to costliest is. A sequence is finite exactly when that list of positions runs out, as it does at over 20 or at month 12.
Tip: the three dots … are what separate a finite sequence from an infinite one. 6, 12, 24, 48, 96 has five terms and ends; 6, 12, 24, 48, 96, … never does.
Q2.
[Fig. 8.1] Can you draw the patterns for the next two terms of the sequence?
Answer

Fig. 8.1 shows the first five triangular numbers 1, 3, 6, 10, 15 as triangular arrays of dots. The next two terms are 21 and 28, drawn by adding one more row each time.

t₆ = 21t₇ = 28
The sixth and seventh triangular arrays. The sixth has rows of 1, 2, 3, 4, 5, 6 dots; the seventh adds a bottom row of 7.
t6 = 1 + 2 + 3 + 4 + 5 + 6 = 21
t7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
Why it happens: to go from one triangular array to the next you keep the whole of the old triangle and lay a fresh row underneath it. That new row has one dot more than the row above, so the count grows by 15 + 6 = 21 and then by 21 + 7 = 28. This is why each triangular number equals the sum of the natural numbers up to its own position.
Q3.
[Fig. 8.2] This interesting relationship between the odd numbers and square numbers can be represented by the diagram in Fig. 8.2. Can you explain the relationship?
Answer

Fig. 8.2 fills a square array of dots with L-shaped bands (gnomons), each one a different colour. The first band is 1 dot, the second 3, the third 5, and so on — so building a square is the same as adding up odd numbers.

A 6 × 6 array split into L-shaped bands of 1, 3, 5, 7, 9 and 11 dots. The grey lines mark where one square ends and the next begins.
1 = 12
1 + 3 = 4 = 22
1 + 3 + 5 = 9 = 32
1 + 3 + 5 + 7 = 16 = 42
1 + 3 + 5 + 7 + 9 + 11 = 36 = 62
Why it happens: to enlarge an n × n square into an (n + 1) × (n + 1) square you must add one new column of n dots, one new row of n dots, and one corner dot — that is n + n + 1 = 2n + 1 dots, which is always an odd number. So each step up the square numbers costs exactly one more odd number, and the sum of the first n odd numbers must be n2. The picture is not an illustration of the fact; it is the proof.
Try This: add the first 10 odd numbers without adding them. The answer is 102 = 100.
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