Solve the Sequence Equation: Is 1 a Term in 15n - 20?

Question

15n20 15n-20

Is the number 1 a term in the sequence above?

Video Solution

Solution Steps

00:06 Is number 1 part of the sequence?
00:10 Let's plug the number into the sequence formula and solve for N.
00:15 If N is a positive whole number, then it's the position in the sequence.
00:22 Now, let's isolate N in the equation.
00:34 N is positive but not a whole number. So, the number is not part of the sequence.
00:41 And that's how we solve this problem!

Step-by-Step Solution

To determine if the number 1 is a term in the sequence given by 15n20 15n - 20 , we set the expression equal to 1:

15n20=1 15n - 20 = 1

Now, solve for n n :

15n20+20=1+20 15n - 20 + 20 = 1 + 20
15n=21 15n = 21

Divide both sides by 15 to solve for n n :

n=2115 n = \frac{21}{15}

Simplify the fraction:

n=75 n = \frac{7}{5}

The result, n=75 n = \frac{7}{5} , is not an integer. Since n n must be a positive integer in sequence indexing, there is no valid solution for integer n n . Therefore, the number 1 cannot be a term of this sequence.

The correct answer is No.

Answer

No.