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AQA GCSE · Question 22.1 · Algebra
Write the missing term in the geometric progression.
1, 4, 16, __, 256
Write the missing term in the geometric progression.
1, 4, 16, __, 256
How to approach this question
1. **Identify the pattern:** A geometric progression has a common ratio between consecutive terms.
2. **Find the common ratio:** Divide a term by the previous term.
4 ÷ 1 = 4.
16 ÷ 4 = 4.
The common ratio is 4.
3. **Find the missing term:** Multiply the previous term (16) by the common ratio (4).
16 × 4 = 64.
4. **Check the next term:** Multiply the missing term (64) by the common ratio (4).
64 × 4 = 256. This matches the last term in the sequence, so the answer is correct.
Full Answer
64
A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The sequence is 1, 4, 16, __, 256.
To find the common ratio (r), we can divide any term by its preceding term.
r = 4 / 1 = 4
Let's check with the next pair:
r = 16 / 4 = 4
The common ratio is indeed 4.
To find the missing term, we multiply the term before it (16) by the common ratio (4).
Missing term = 16 × 4 = 64.
We can verify this by checking if multiplying our result by 4 gives the next term in the sequence.
64 × 4 = 256. This is correct.
So the missing term is 64.
Common mistakes
✗ Thinking it is an arithmetic progression and trying to add a constant difference.\n✗ Making a multiplication error (e.g., 16 x 4 = 60).
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