Question 78(i)

Observe the toothpick pattern given below
Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
$\begin{matrix} P a t t e r n & 1 & 2 & 3 & 4 & 5 & 6 T o o t h p i c k s & 4 & 13 \end{matrix}$

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Solution

The relationship between the pattern number and the number of matchsticks in it is as follows:
$P a t t e r n 1 \to 4 P a t t e r n 2 \to 7 = 4 + 3 = P a t t e r n 1 + 3 P a t t e r n 3 \to 10 = 7 + 3 = P a t t e r n 2 + 3 P a t t e r n 4 \to 13 = 10 + 3 = P a t t e r n 3 + 3$

Using this relationship, we can find the number of matchsticks in pattern 5 and 6.
$P a t t e r n 5 = P a t t e r n 4 + 3 = 13 + 3 = 16 P a t t e r n 6 = P a t t e r n 5 + 3 = 16 + 3 = 19$

Table:
$\begin{matrix} P a t t e r n & 1 & 2 & 3 & 4 & 5 & 6 T o o t h p i c k s & 4 & 7 & 10 & 13 & 16 & 19 \end{matrix}$

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Similar questions

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Q. Question 78(iii)

Observe the toothpick pattern given below.

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Q. Question 78(iv)
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Question 128(i)

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Powers Table
$\begin{matrix} X & 1^{x} & 2^{x} & 3^{x} & 4^{x} & 5^{x} & 6^{x} & 7^{x} & 8^{x} & 9^{x} & 10^{x} 1 & 1 & 2 2 & 1 & 4 3 & 1 & 8 4 & 1 & 16 5 & 1 & 32 6 & 1 & 64 7 & 1 & 128 8 & 1 & 256 Ones digits of the powers & 1 & 2, 4, 6, 8 \end{matrix}$
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Question 78(i) Observe the toothpick pattern given below Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms. Pattern123456Toothpicks413

Question 78(i)

Observe the toothpick pattern given below
Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
$\begin{matrix} P a t t e r n & 1 & 2 & 3 & 4 & 5 & 6 T o o t h p i c k s & 4 & 13 \end{matrix}$