Question

4. A sequence is formed by the matchsticks as shown below
a) Write the number of matchsticks in the terms as a sequence ?
b) This is an arithmetic sequence. What is its algebraic form?
c) How many matchsticks are there in its 10 th term?​

Answer 1

Answer:

Pattern associated with the number of matchsticks:

Figure 1: No. of sticks =3=3+0

Figure 2: No. of sticks =5=3+2

Figure 3: No. of sticks =7=3+2+2

Figure 4: No. of sticks =9=3+2+2+2

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The rule associated with it can be given as no. of sticks =3+2(n−1) where n is the number of the figure.

Now there are 97 matchsticks

⟹3+2(n−1)=97

⟹3+2n−2=97

⟹2n=96

⟹n=48

Hence, serial number of the figure having 97 matchsticks is 48.