# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/16

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Question 16

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## Exercise 16

### Question

export const metadata = {
  title: "Question 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Consider the following number sequence:

<BlockMath math="0.5, \ 3, \ 8, \ 18, \ 38, \ 78, \ \dots, \ 318" />

The correct number to complete the pattern is ...


### Choices

- [ ] $$120$$
- [x] $$158$$
- [ ] $$160$$
- [ ] $$168$$
- [ ] $$200$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Question 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The given number sequence is:

<BlockMath math="0.5, \ 3, \ 8, \ 18, \ 38, \ 78, \ \dots, \ 318" />

Let's analyze the difference between consecutive terms:

<MathContainer>
  <BlockMath math="3 - 0.5 = 2.5" />
  <BlockMath math="8 - 3 = 5" />
  <BlockMath math="18 - 8 = 10" />
  <BlockMath math="38 - 18 = 20" />
  <BlockMath math="78 - 38 = 40" />
</MathContainer>

Observing the pattern of differences (<InlineMath math="2.5, \ 5, \ 10, \ 20, \ 40" />), we can see that each difference is obtained by multiplying the previous difference by <InlineMath math="2" /> (a common ratio of <InlineMath math="2" />).

Therefore, the next difference after <InlineMath math="40" /> is:

<BlockMath math="40 \times 2 = 80" />

Thus, the number that fills the blank is:

<BlockMath math="78 + 80 = 158" />

To verify this pattern, let's calculate the subsequent term and check if it matches the last known term (<InlineMath math="318" />). The next difference after <InlineMath math="80" /> would be <InlineMath math="80 \times 2 = 160" />.

<BlockMath math="158 + 160 = 318" />

The calculation matches the last term in the problem.

Therefore, the correct number to complete the pattern is <InlineMath math="158" />.


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