For each pattern shown below, (i) Draw the next figure in the sequence. (ii) How many basic units are there in Step 10? Class 8

For each pattern shown below, (i) Draw the next figure in the sequence. (ii) How many basic units are there in Step 10? Class 8

Question 1.

For each pattern shown below, Class 8

(i) Draw the next figure in the sequence.

(ii) How many basic units are there in Step 10?

(iii) Write an expression to describe the number of basic units in Step y.

Solution:

(ii) In step 10, in the first figure, number of basic units are (10 - 2)² = 8² = 64.

In the second figure, number of basic units are 10th term of the sequence 5, 11, 19, 29, ...,

i. e., of 5, (5 + 6), (11 + 8), (19 + 10), (29 + 12), (41 + 14), (55 + 16), (71 + 18) = 89, (89 + 20) = 109, (109 + 22) = 131.

i. e., 131 or (10 + 1)² + 10 = 121 + 10 = 131

(iii) In the first figure, number of basic units in step y = (y - 2)² = y² - 4y + 4.

In the second figure, number of basic units in step y=(y + 1)² + y = y² + 2y + 1 + y

= y² + 3y + 1.