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

Complete the sequence according to the rule $2n-1$.

._ , _ , 5 , 3 , 1

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.