Find the 10th and nth terms of the GP: 5, 25, 125, … .

Step-by-step solution

Idea: a = 5 and r = 255 = 5. Use t_n = arⁿ⁻¹.

1. a = 5, r = 255 = 5.½ mark
2. t_n = 5 × 5ⁿ⁻¹ = 5ⁿ.½ mark
3. t₁₀ = 5¹⁰ = 9765625.1 mark

Check: n = 3: 5³ = 125 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing the nth term as 5ⁿ⁻¹ (which gives 1 for the first term).
• Computing 5¹⁰ as 5 × 10 = 50.
• Writing 5 × 5ⁿ⁻¹ = 25ⁿ⁻¹. Multiply powers of the same base by adding exponents: 5¹ × 5ⁿ⁻¹ = 5ⁿ.

How this can come in the exam

Try one yourself

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