# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/10

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Question 10

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## Exercise 10

### Question

export const metadata = {
  title: "Question 10",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given <InlineMath math="a_1 = 8" />, <InlineMath math="a_2 = -5" />, and <InlineMath math="a_{n+1} = a_{n+2} - 4a_n" />. The value of <InlineMath math="a_3 + a_4" /> is ....


### Choices

- [ ] $$10$$
- [ ] $$20$$
- [ ] $$24$$
- [x] $$34$$
- [ ] $$44$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 10",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given the recursive equation:

<MathContainer>
  <BlockMath math="a_{n+1} = a_{n+2} - 4a_n" />
</MathContainer>

We can rearrange the equation to find <InlineMath math="a_{n+2}" />:

<MathContainer>
  <BlockMath math="a_{n+2} = a_{n+1} + 4a_n" />
</MathContainer>

**Step 1**: Find the value of <InlineMath math="a_3" /> by substituting <InlineMath math="n = 1" />. Given <InlineMath math="a_1 = 8" /> and <InlineMath math="a_2 = -5" />.

<MathContainer>
  <BlockMath math="a_{1+2} = a_{1+1} + 4a_1" />
  <BlockMath math="a_3 = a_2 + 4a_1" />
  <BlockMath math="a_3 = -5 + 4(8)" />
  <BlockMath math="a_3 = -5 + 32" />
  <BlockMath math="a_3 = 27" />
</MathContainer>

**Step 2**: Find the value of <InlineMath math="a_4" /> by substituting <InlineMath math="n = 2" />.

<MathContainer>
  <BlockMath math="a_{2+2} = a_{2+1} + 4a_2" />
  <BlockMath math="a_4 = a_3 + 4a_2" />
  <BlockMath math="a_4 = 27 + 4(-5)" />
  <BlockMath math="a_4 = 27 - 20" />
  <BlockMath math="a_4 = 7" />
</MathContainer>

**Step 3**: Calculate the sum <InlineMath math="a_3 + a_4" />.

<MathContainer>
  <BlockMath math="a_3 + a_4 = 27 + 7" />
  <BlockMath math="a_3 + a_4 = 34" />
</MathContainer>

So, the value of <InlineMath math="a_3 + a_4" /> is <InlineMath math="34" />.


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