Question

Identify the rule and find the next term in the following patterns. Also, write the expression for the $n^{th}$ term of the pattern.

Answer 1

Finding the pattern.

We observe the given pattern and we get,

In the first term, we have $3$ petals, where $3=(2\times 1)+1$

In the second term, we have $5$ petals, where $5=(2\times 2)+1$

In the third term, we have $7$ petals, where $7=(2\times 3)+1$

In fourth term, we have $9$ petals, where $9=(2\times 4)+1$

This means that each term has $2$ more petals than its previous term

Thus, if we continue like this that we observe that the next term will have $11$ petals in it, where $11=(2\times 5)+1$

Also, we observe the number of petals in each term $=(2\times$number of terms that we need to find$)+1$

Therefore, the expression for $n^{th}$ term will be $=2\mathrm{n}+1$, where $2\mathrm{n}+1$ denotes the number of petals in $n^{th}$ term.

Hence, the expression for $n^{th}$ term will be $2\mathrm{n}+1$.