Question

Aim: Given a figure

Think About It: Emari was waiting for his friend at a café, got bored, and started to make patterns out of toothpicks while he waited.
Explain what is happening below and use any method to determine how many toothpicks would be in Pattern 10. Explain how you
determined the answer.
Pattern 1
4 tonthpicks
Pattern 2
7 toothpicks
Pattern 3
10 toothpicks

Answer 1

• 31 toothpicks

Task :

• To work out the number of toothpics in Patten 10

Solution :

we are given that the number of toothpics in Patten 1 are 4 and each pattern is getting succeeded by 3 more toothpics thus to find the number of toothpics in Patten 10 we can use this formula

• 
  `a_n = a_1 + (n - 1)d`

wherein,

• a_n = nth term (10)
• a_1 = first term (4)
• n = number of terms (10)
• d = difference between the first and the second term (7-4 = 3)

Plugging in the values ,

• 
  `a_(10)= 4+ (10 - 1)3`
• 
  `a_(10)= 4 + 27`
• 
  `a_(10) = 31`

Therefore,there would be a total of 31 toothpicks in the 10th pattern of the sequence created by Emari.