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Arithmetic Progressions
NCERT Exemplar
CBSE
Grade 10

Question:

If $7$ times the $7^{\text{th}}$ term of an AP is equal to $11$ times its $11^{\text{th}}$ term, then its $18^{\text{th}}$ term will be:
(a) $7$
(b) $11$
(c) $18$
(d) $0$

Step-by-Step Solution

Key Concept: If $m \cdot a_m = n \cdot a_n$, then $a_{m+n} = 0$.
$7(a + 6d) = 11(a + 10d) \Rightarrow 7a + 42d = 11a + 110d$. [0.5 Mark]
$4a + 68d = 0 \Rightarrow 4(a + 17d) = 0 \Rightarrow a_{18} = a + 17d = 0$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Forming equation $7(a+6d) = 11(a+10d)$: 0.5 Mark
Simplifying to $a + 17d = 0 \Rightarrow a_{18} = 0$: 0.5 Mark

Correct Answer: $0$
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