Is 10 a Term in the Sequence Defined by 4n+3?

Question

A sequence has the rule 4n+3 4n+3 .

Is the number 10 a term in the sequence?

Video Solution

Solution Steps

00:06 Is the number 10 part of this sequence?
00:10 Let's plug it into the sequence formula and find N.
00:14 If we get a positive whole number for N, it's a match!
00:18 Okay, now let's carefully isolate N.
00:34 We found N is positive but not whole, so 10 isn't in the sequence.
00:40 And that's the answer to our question!

Step-by-Step Solution

To solve whether 10 is a term in the sequence defined by 4n+3 4n + 3 , follow these steps:

  • Step 1: Start with the equation for the sequence, 4n+3=10 4n + 3 = 10 .
  • Step 2: Subtract 3 from both sides to isolate the term with n n . This gives 4n=7 4n = 7 .
  • Step 3: Divide both sides by 4 to solve for n n . This results in n=74 n = \frac{7}{4} .

Since n=74 n = \frac{7}{4} , which is not an integer, it confirms that 10 is not a term in the sequence 4n+3 4n + 3 . For a number to be a term in this sequence, n n must be an integer. Thus, 10 is not part of the sequence because it does not satisfy this condition.

Therefore, the number 10 is not in the sequence.

The correct answer choice is:

  • Choice 4:

    No

Answer

No