The figure below shows a sequence of patterns that consists of stars. A table of summary is given as

Question

The figure below shows a sequence of patterns that consists of stars. A table of summary is given as well. Pattern number, ${n}$Number of stars, ${s}$ ${1}$${1}$ ${2}$${5}$ ${3}$${9}$ $\vdots$$\vdots$ ${n}$${?}$ Calculate the number of stars in Pattern ${5}$. Express, in terms of ${n}$, for finding the number of stars in Pattern ${n}$. Find ${n}$ if the pattern contains ${77}$ stars.

Accepted Answer

(a) $17$ (b) $s=4n-3$ (c) $n=20$

Pattern number, \({n}\)	Number of stars, \({s}\)
\({1}\)	\({1}\)
\({2}\)	\({5}\)
\({3}\)	\({9}\)
\(\vdots\)	\(\vdots\)
\({n}\)	\({?}\)

Star Pattern: Number of Stars in Each Diagram

Star Pattern: Number of Stars in Each Diagram

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