A sequence of patterns formed by circles is shown below. Draw Pattern $5$. Complete the following

Question

A sequence of patterns formed by circles is shown below. Draw Pattern $5$. Complete the following table: Based on your answers in (ii), find the number of circles in the lowest line and the total number of circles, respectively, in pattern $39$. the total number of circles, $T_n$, in the pattern where the number of circles in the lowest line, $k$, is $100$.

Accepted Answer

(i) Pattern 5 has five rows with $5$ circles in the lowest row (ii) $k_n=n$, $T_n=\frac{n(n+1)}{2}$ (iii)(a) $39$ and $780$ (iii)(b) $5050$

Number Patterns

Number Patterns

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