Find Position of 9 in Sequence 2n+2: Term Identification Problem

Question

Given a formula with a constant property that depends on $n$ :

$2n+2$

Is the number 9 Is it part of the series? If so, what element is it in the series?

Video Solution

Solution Steps

00:00 Is the number 9 a member of the sequence? And if so, what is its position?

00:03 Let's substitute the desired member into the sequence formula and solve

00:09 If the solution for N is positive and whole, the number is a member at position N in the sequence

00:13 Let's isolate N

00:25 We can see that the solution for N is positive, but not a whole number

00:28 Therefore, the number is not a member of the sequence

00:32 And this is the solution to the question

Step-by-Step Solution

To determine if 9 is part of the sequence given by the formula $2n + 2$ , we need to solve the equation for $n$ :

$2n + 2 = 9$

Subtract 2 from both sides:

$2n = 7$

Divide both sides by 2:

$n = \frac{7}{2}$

The solution $n = \frac{7}{2}$ is not an integer, meaning there is no integer $n$ such that $2n + 2 = 9$ . Therefore, the number 9 is not part of the sequence.

In conclusion, the number 9 does not belong in the sequence defined by $2n + 2$ , so the answer is No.

Answer

Related Subjects

Recurrence Relations Sequences