Bookmarks Window Help ? docs.google.com 5 Summer Life H.. How To Go From Your Be

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Bookmarks Window Help ? docs.google.com 5 Summer Life H.. How To Go From Your Best Friend. Search results -... Age Consider star shapes with p vertices, leading to p-star numbers. The first four representations for a star with 6 vertices are shown in the four stages S, to S, below. The 6-star number at each stage is the total number of dots in the diagram. Si S2 s, Sa Find the number of dots (the star number) for at least 6 stages. Organise the data and look for patterns. Look for the general term for a 6-star number (a star with 6 vertices at stage S.). Now repeat the process for other values of p. This means, find similar data for other stars with different numbers of vertices. Then find the general term. Hence, produce the general statement, in terms of p and n, that generates the sequence of ? MacBook Air

Explanation / Answer

The number of dots for atleast 6 stages is given below

S1 = 1 (dot)

S2 = 1 + 12 (dots) = 13 dots

S3 = 1 + 12 + 2 * 12 (dots) = 37 dots

S4 = 1 + 12 + 2 * 12 + 3 * 12 = 73 dots

S5 = 1 + 12 + 2 * 12 + 3 * 12 + 4 * 12 = 121 dots

S6 = 1 + 12 + 2 * 12 + 3 * 12 + 4 * 12 + 5 * 12 = 181 dots

Now seeing the data and looking for patterns

Sn = 1 + 12 + 2 * 12 + ... + (n-1) * 12 = 1 + 12(1+2+3+...+(n-1)) = 1 + 12(n-1)(n)/2 = 1 + 6n(n-1) = 1 + 6n^2 - 6n = 6n^2 - 6n + 1

Similarly for p star the logic will be

Sn = 1 + 2p + 2 * 2p + 3 * 2p + ... + (n-1) * 2p = 1 + 2p(1+2+3.+...+(n-1)) = 1 + 2p * n * (n-1)/2 = 1 + pn^2 - pn

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