Maths ·Class 9 Maths

Verify that the following sequences are arithmetic progressions and write their nth terms. Class 9

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· Jul 10, 2026 · Reviewed & updated Sep 17, 2026 · 1 min read

Verify that the following sequences are arithmetic progressions and write their nth terms. Class 9

Question 1.

Verify that the following sequences are arithmetic progressions and write their n^th terms. What do you observe when you plot the ordered pairs emerging from them? Class 9

i. 2, 5, 8, 11.

ii. -5, -1, 3, 7...

Answer:

i. Given sequence: 2, 5, 8, 11, ...

Here, 5 - 2 = 8 - 5 = 11 - 8 = 3

Difference between two consecutive terms is same

So, it is an Arithmetic Progression with First term (a) = 2 and Common difference (d) = 3.

n^th term of sequence is

t_n = 2 + (n - 1) × 3

∴ t_n = 3n - 1

ii. Given sequence: -5, -1, 3, 7, ...

Here, -1 - (-5) = 3 - (-1)

= 7 - 3

= 4

∴ Difference between two consecutive terms is same

So, it is an Arithmetic Progression with First term (a) = -5 and

Common difference (d) = 4.

n^th term of sequence is

t_n = -5 + (n - 1) × 4

∴ t_n = 4n - 9.

Below we have plot the graph of ordered pair obtained from both sequences.

x	1	2	3	4
y	2	5	8	11
(x, y)	(1, 2)	(2, 5)	(3, 8)	(4, 11)

ii.

x	1	2	3	4
y	-5	-1	3	7
(x, y)	(1, -5)	(2, -1)	(3, 3)	(4, 7)

Observation:

When the ordered pairs are plotted on a graph, the points lie on a straight line, showing a linear pattern.