CBSE Class 10 Maths (Standard) 2022 · Paper 30/1/1 · Question 13

Arithmetic Progressions 4 marks Medium

In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression :

Figure 3 of the matchstick pattern.

Figure 2 of the matchstick pattern.

Figure 1 of the matchstick pattern.

aWrite the AP for the number of triangles used in the figures. Also, write the $n^{t h}$ term of this AP.[2]
bWhich figure has 61 matchsticks ?[2]

Answer

(a) Triangle AP:

4, 6, 8, \dots

a_{n} = 2 n + 2

. (b) Matchstick AP

12, 19, 26, \dots

has

a_{n} = 7 n + 5

;

7 n + 5 = 61 \Rightarrow n = 8

, so Figure

8

has

61

matchsticks.

🔒 Step-by-step solution

From the board paper

CBSE Class 10 Maths (Standard) 2022 · Paper 30/1/1, Question 13 — all 14 questions with answers →

CBSE Class 10 Maths (Standard) 2022 · Paper 30/1/1 · Question 13

Answer

From the board paper

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