For what value of $n$, are the $n$th terms of the APs: $9, 7, 5, \ldots$ and $15, 12, 9, \ldots$ the same?
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
For AP: 9, 7, 5, … → $a = 9$, $d = -2$
$a_n = 9 + (n-1)(-2) = 11 - 2n$
For AP: 15, 12, 9, … → $a = 15$, $d = -3$
$a_n = 15 + (n-1)(-3) = 18 - 3n$
Setting them equal:
$$11 - 2n = 18 - 3n$$
$$n = 7$$
∴ The 7th terms of both APs are equal.
Source: Chapter 5, Exercise 5.2 (Q.15 type); Section 5.3 – nth term formula
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Explanation
- Write the $n$th term formula $a_n = a + (n-1)d$ for each AP separately.
- Equate the two expressions and solve for $n$.
- Examiners award 1 mark for correctly setting up both $a_n$ expressions and 1 mark for solving $n = 7$.
- Always verify: $a_7$ for AP1 = $11-14 = -3$; $a_7$ for AP2 = $18-21 = -3$. ✓