Complete the Odd Integer Series: Identifying the Missing Numbers in 2n-1

Question

Complete the series for the series. 2n1 2n-1

1,3,5,,. 1,3,5,_—,_—.

Video Solution

Solution Steps

00:00 Complete the missing terms
00:03 Identify the location of the missing terms
00:16 Substitute the desired term's position in the sequence formula and solve
00:21 Always solve multiplication and division before addition and subtraction
00:26 This is the fourth term in the sequence
00:29 Use the same method to find the fifth term
00:33 Substitute the desired term's position in the sequence formula and solve
00:38 Always solve multiplication and division before addition and subtraction
00:45 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's analyze the sequence defined by 2n12n - 1, which produces a series of odd numbers. We can identify each term as follows:

  • First term (n=1n = 1): 2×11=12 \times 1 - 1 = 1
  • Second term (n=2n = 2): 2×21=32 \times 2 - 1 = 3
  • Third term (n=3n = 3): 2×31=52 \times 3 - 1 = 5
  • Fourth term (n=4n = 4): 2×41=72 \times 4 - 1 = 7
  • Fifth term (n=5n = 5): 2×51=92 \times 5 - 1 = 9

Therefore, the two missing numbers in the sequence after 5 are 7 and 9, following the pattern of odd numbers.

The series is thus completed to be: 1,3,5,7,91, 3, 5, 7, 9.

In examining the given choices, the correct answer is 7,97, 9.

Answer

7,9