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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 1 · Q13
In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used…
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 $\displaystyle 1$ Figure $\displaystyle 2$ Figure $\displaystyle 3$
(a)
Write the AP for the number of triangles used in the figures. Also, write the $\displaystyle \mathrm{n}^{\text {th }}$ term of this AP.
(b)
Which figure has $\displaystyle 61$ matchsticks ?
Marking-scheme solution
(a) Number of triangles in figures are $\displaystyle 4$, $\displaystyle 6$, 8...
This is an A.P. with \(\displaystyle a=4, d=2\)
\[\therefore a_{n}=4+(n-1) \times 2=2 n+2
\]
(b) Number of matchsticks in figures are $\displaystyle 12$, $\displaystyle 19$, 26...
This is an A.P. with \(\displaystyle a=12, d=7\)
\[\begin{gathered}
\therefore 61=12+(n-1) \times 7 \\
\Rightarrow n=8
\end{gathered}
\]All Arithmetic Progressions questions2022 question paperNCERT solutions: Arithmetic ProgressionsPractice Arithmetic Progressions →
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.