Find the 10th and 15th terms of the sequence t_n = 5n − 3 for n ≥ 1.

Step-by-step solution

Idea: In an explicit rule, put the position number in place of n.

1. t₁₀ = 5 × 10 − 3 = 50 − 3 = 47.1 mark
2. t₁₅ = 5 × 15 − 3 = 75 − 3 = 72.1 mark

Check: From the 10th to the 15th term is 5 steps of 5: 47 + 25 = 72 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing 5 × 10 − 3 as 5 × 7 = 35 (subtracting before multiplying).
• Listing terms 2, 7, 12, … by hand and miscounting the position.
• Writing t₁₀ = 10 instead of finding the term in position 10.

How this can come in the exam

Try one yourself

Find the 12th and 30th terms of t_n = 4n + 7.

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