Pattern with Black Circles

Transcript

Pattern with Black CirclesLet’s observe this pattern below We have to answer a few questions Draw the next figure in the sequence. How many circles does it have? How many total circles are there in Step 10? Write an expression for the number of circles in Step k. Now, there are many ways of interpreting this patter. Let’s look at some of them Method 1 Number of Circles = (Step Number + 1)2 – 1 Now, here the Number of Circles are Number of circles = (k + 1)2 – 1 = k2 + 2 × k × 1 + 12 – 1 = k2 + 2k Method 2 Number of Circles = Step Number2 + 2 × Step Number Now, here the Number of Circles are Number of circles = k2 + 2kMethod 3 Number of Circles = Step Number × (Step Number + 1) + Step Number Now, here the Number of Circles are Number of circles = k × (k + 1) + k = k2 + k + 2 = k2 + 2kMethod 4 Number of Circles = Step Number × (Step Number + 2) Now, here the Number of Circles are Number of circles = k × (k + 2) = k2 + 2k Method 4 Number of Circles = Step Number × (Step Number + 2) Now, here the Number of Circles are Number of circles = k × (k + 2) = k2 + 2k