Solve n-0.5n Sequence: Finding Position of Number 5

Question

Given a formula with a constant property that depends onn n :

n−0.5n n-0.5n

Is the number 5 Is it part of the series? If so, what element is it in the series?

Video Solution

Solution Steps

00:00 Is the number 5 a member of the sequence? If yes, what is its position?
00:03 Let's substitute the desired term into the sequence formula and solve
00:06 If the solution for N is positive and whole, the number is a term at position N in the sequence
00:12 Let's isolate N
00:27 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify the expression n−0.5n n - 0.5n .
  • Step 2: Set up the equation for 5 using the simplified formula.
  • Step 3: Solve for n n .
  • Step 4: Verify the solution.

Now, let's work through each step:
Step 1: Given the expression n−0.5n n - 0.5n , it simplifies to 0.5n 0.5n .
Step 2: Set up the equation 0.5n=5 0.5n = 5 .
Step 3: Solve for n n :
To find n n , we multiply both sides of the equation by 2:
n=10 n = 10 .
Step 4: Verification:
Substitute n=10 n = 10 back into the simplified formula: 0.5⋅10=5 0.5 \cdot 10 = 5 , which confirms that 5 is part of the sequence.

Therefore, the number 5 is indeed part of the sequence, and it corresponds to n=10 n = 10 .

Yes, 10 10

Answer

Yes, 10 10

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Recurrence Relations Sequences