Complete the Sequence Using Formula 2n-1: Finding Missing Terms

Video Solution

Solution Steps

00:00 Complete the sequence

00:06 Find the appropriate element positions

00:12 Substitute the element position in the sequence formula to find the element

00:16 Substitute N = 4 in the sequence formula

00:28 Always solve multiplication and division before addition and subtraction

00:31 This is the fourth element in the sequence

00:41 We'll use the same method to find the fifth element in the sequence

00:47 Substitute N = 4 in the sequence formula

00:56 And this is the solution to the question

Step-by-Step Solution

To solve the problem of completing the sequence using the rule $2n - 1$ , follow these steps:

Step 1: Recognize that each term in the sequence is represented by the formula $2n - 1$ . The provided sequence is in reverse order: 5, 3, 1.
Step 2: Identify the value of $n$ that results in each of these terms.
- For term 5: $2n - 1 = 5$ implies $2n = 6$ , thus $n = 3$ .
- For term 3: $2n - 1 = 3$ implies $2n = 4$ , thus $n = 2$ .
- For term 1: $2n - 1 = 1$ implies $2n = 2$ , thus $n = 1$ .
Step 3: Consider the terms preceding the known sequence, calculating them for $n = 4$ and $n = 5$ :
- For $n = 4$ , $2n - 1 = 2 \cdot 4 - 1 = 7$ .
- For $n = 5$ , $2n - 1 = 2 \cdot 5 - 1 = 9$ .
Step 4: Identify the missing numbers to complete the sequence: 9 and 7 must be placed before the given sequence 5, 3, 1.

Therefore, the completed sequence, according to the rule $2n - 1$ , is 9, 7, 5, 3, 1.