Question

A pattern is made by toothpick squares. Select the series that represents the number of toothpicks added to a picture to get the next picture to the right. Pretend the first picture has no toothpicks.

1st square made of 4 toothpicks, second made of 12, 3rd made of 24, 4th made of 40 toothpicks.

Q.1 Write a series in summation notation for the total number of toothpicks in a square with a side length of 6 toothpicks.
Q.2 How many toothpicks are required to form the large square with 6 toothpicks on a side? (Hint: Evaluate the series in the previous question.

Answer 1

\[a_n= a_{n-1}+4n\]

Answer 2

tq