Question

How many dots are in the nth term of the following sequence?OTerm:234Choose the correct answer below.O A. n2+2OB. 2n + 1O C. n + 3OD. n +2

Answer 1

Given:

The dots of first, second, third, ... terms are shown.We have to find the dots in the nth term.

The sequence is given as:

`3,5,7,9,\ldots\text{.}`

Hence, first term is 3 here,so a=3

Now , the sequence is an arithmetic sequence with common difference as 2.

So d=2 here.

The nth term is given by the explicit formula:

`a_n=a+(n-1)d`

Substituting the values,

`\begin{gathered} a_n=3+(n-1)2 \\ =3+2n-2 \\ =2n+1 \end{gathered}`

Hence, there will be (2n+1) dots in the nth term

Hence, Option B is true.