Is 1, 2, 4, 8, 16, … 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: 21 = 2, 42 = 2, 84 = 2, 168 = 2.1 mark
2. All the ratios are equal, so the sequence is a GP with common ratio 2.1 mark

Check: First term × ratio repeatedly: 1, 1 × 2 = 2, … reproduces the sequence ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing the common ratio as 1 + 1 or as a difference (2 − 1 = 1). A GP uses ratios (division), not differences.
• Checking only the first pair. Check every consecutive pair.
• Dividing the wrong way round (12). Divide each term by the term before it.

How this can come in the exam

Try one yourself

Is 4, 8, 16, 32, … a GP? If so, find the common ratio.

More questions like this

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

All Sequences and progressions questions · All maths questions