Question 11 - Pattern 2 - Figure it out - Page 154-156 - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Question 11 – Pattern 2 For each pattern shown below, (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.Analysing the pattern Step 1: It is a square of 2 × 2 With one additional unit squares Total squares = 2 × 2 + 1 = 5 Step 2: It is a square of 3 × 3 With two additional unit squares Total squares = 3 × 3 + 2 = 11 Step 3: It is a square of 4 × 4 With three additional unit squares Total squares = 4 × 4 + 3 = 19 Thus, In Step 4 It is a square of 5 × 5 With four additional unit squares Total squares = 5 × 5 + 4 = 29 Thus, we can say that Number of squares in step y = (y + 1)2 + y And, Number of unit squares in step 10 = (10 + 1)2 + 10 = 112 + 10 = 121 + 10 = 131