Question 6 of 51beginner🔧 ApplyNumerical3 marks

Using the explicit rule un=2n−1u_n = 2n - 1, find the 53rd53^{rd} term, the 108th108^{th} term, and the 1170th1170^{th} term of the odd number sequence.

Correct Answer

(108th term) 215

(1170th term) 2339

(53rd term) 105

Exercise: Exercise | Q: 1 | (Page 4)
For More Understanding

Explanation

To find the specific terms of the odd number sequence, we use the explicit rule un=2n−1u_n = 2n - 1. An explicit formula allows us to find any term directly by substituting the appropriate value of nn without needing to know the previous terms.

Step 1: Finding the 53rd term - Substitute n=53n = 53 into the formula: u53=2(53)−1=106−1=105u_{53} = 2(53) - 1 = 106 - 1 = 105. Step 2: Finding the 108th term - Substitute n=108n = 108 into the formula: u108=2(108)−1=216−1=215u_{108} = 2(108) - 1 = 216 - 1 = 215. Step 3: Finding the 1170th term - Substitute n=1170n = 1170 into the formula: u1170=2(1170)−1=2340−1=2339u_{1170} = 2(1170) - 1 = 2340 - 1 = 2339.

Therefore, the 53rd term is 105, the 108th term is 215, and the 1170th term is 2339.

Solution Steps

  1. Step 1: Substitute n = 53 into u_n = 2n - 1: u_53 = 2(53) - 1 = 105

  2. Step 2: Substitute n = 108 into u_n = 2n - 1: u_108 = 2(108) - 1 = 215

  3. Step 3: Substitute n = 1170 into u_n = 2n - 1: u_1170 = 2(1170) - 1 = 2339

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