# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/2

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 2

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## Exercise 2

### Question

export const metadata = {
  title: "Problem 2",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

<InlineMath math="42, 40, 39, 36, 34, 30, 27, 22, ..., ..." />


### Choices

- [ ] $$21, 15$$
- [ ] $$20, 14$$
- [ ] $$19, 13$$
- [x] $$18, 12$$
- [ ] $$18, 11$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 2",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The sequence above consists of two alternating sub-sequences (skipping one number).

#### Pattern 1 (Odd positions)

<InlineMath math="42, 39, 34, 27, ..." />

The differences between consecutive terms are:

<BlockMath math="\begin{aligned} 39 - 42 &= -3 \\ 34 - 39 &= -5 \\ 27 - 34 &= -7 \end{aligned}" />

The pattern is subtracting consecutive odd numbers (<InlineMath math="-3, -5, -7" />). Thus, the next difference is <InlineMath math="-9" />. Next term: <InlineMath math="27 - 9 = 18" />.

#### Pattern 2 (Even positions)

<InlineMath math="40, 36, 30, 22, ..." />

The differences between consecutive terms are:

<BlockMath math="\begin{aligned} 36 - 40 &= -4 \\ 30 - 36 &= -6 \\ 22 - 30 &= -8 \end{aligned}" />

The pattern is subtracting consecutive even numbers (<InlineMath math="-4, -6, -8" />). Thus, the next difference is <InlineMath math="-10" />. Next term: <InlineMath math="22 - 10 = 12" />.

So, the next two numbers are <InlineMath math="18" /> and <InlineMath math="12" />.


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