Find the 12th term of a GP with common ratio 2, whose 8th term is 192.

Step-by-step solution

Idea: From the 8th term to the 12th term is 4 steps, and each step multiplies by r = 2. So multiply 192 by 2⁴.

1. t₈ = ar⁷ = 192 and t₁₂ = ar¹¹ = ar⁷ × r⁴.1 mark
2. t₁₂ = 192 × 2⁴ = 192 × 16 = 3072.1 mark

Check: First term a = 192 ÷ 2⁷ = 1.5; then 1.5 × 2¹¹ = 1.5 × 2048 = 3072 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Multiplying by 2 only once or by 2 × 4 = 8 (getting 1536). Four steps of ×2 give ×16.
• Treating it as an AP and adding: 192 + 4 × 2 = 200.
• Using 2⁵ by counting the terms 8, 9, 10, 11, 12 instead of the steps between them.

How this can come in the exam

Try one yourself

The 6th term of a GP with common ratio 2 is 96. Find its 10th term and its first term.

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