Using the explicit rule u_n = 2n − 1, find the 53rd term, the 108th term, and the 1170th term of the odd number sequence.

Step-by-step solution

Idea: Substitute the position number for n in 2n − 1.

1. u₅₃ = 2 × 53 − 1 = 106 − 1 = 105.½ mark
2. u₁₀₈ = 2 × 108 − 1 = 216 − 1 = 215.½ mark
3. u₁₁₇₀ = 2 × 1170 − 1 = 2340 − 1 = 2339.1 mark

Check: Each answer is odd, and adding 1 then halving gives back the position: (105 + 1) ÷ 2 = 53 ✓, (2339 + 1) ÷ 2 = 1170 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Forgetting to subtract 1 and giving 106, 216, 2340. Those are even, so they cannot be odd numbers.
• Computing 2 × (53 − 1) = 104. Multiply first, then subtract 1.
• Giving the answer as the position (53) instead of the term (105).

How this can come in the exam

Try one yourself

Find the 64th and the 999th odd numbers.

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