Is 1, 3, 9, 27, 81, … a geometric progression? If so, what is the common ratio?

Step-by-step solution

Idea: A sequence is a GP when the ratio (term ÷ previous term) is the same for every pair of consecutive terms. That fixed ratio is the common ratio r.

1. Ratios of consecutive terms: 31 = 3, 93 = 3, 279 = 3, 8127 = 3.1 mark
2. All the ratios are equal, so the sequence is a GP with common ratio 3.1 mark

Check: First term × ratio repeatedly: 1, 1 × 3 = 3, … reproduces the sequence ✓.

Answer to write in the exam

Common mistakes that cost marks

• Taking the ratio as 2 because 3 − 1 = 2. The ratio is 31 = 3.
• Calling the sequence an AP. Its differences are 2, 6, 18, 54, which are not equal.
• Dividing 1 by 3 and giving the ratio as 13.

How this can come in the exam

Try one yourself

Is 5, 15, 45, 135, … a GP? If so, find the common ratio and the next term.

More questions like this

• Is 1, −1, 1, −1, 1, … a geometric progression? If so, what is the common ratio?
• Check whether the sequence 5, 154, 4516, 13564, … is a geometric progression and find its nth term.
• Check whether the following sequences are geometric progressions and find their nth terms.
• Can you find a recursive rule for the formula t_n = 3 × 10ⁿ⁻¹ that generates the geometric progression 3, 30, 300, 3000, … ?
• Observe the Sierpiński triangle and try to answer the following questions

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