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Arithmetic Progressions
RD Sharma
CBSE
Grade 10

Question:

If the $10^{\text{th}}$ term of an A.P. is $52$ and the $17^{\text{th}}$ term is $87$, then its $c^{\text{th}}$ term is given by:
(a) $5c + 2$
(b) $5c - 3$
(c) $5c - 2$
(d) $3c + 5$

Step-by-Step Solution

Key Concept: $a + 9d = 52$ and $a + 16d = 87 \Rightarrow 7d = 35 \Rightarrow d = 5, a = 7$. $a_c = 7 + (c - 1)5 = 5c + 2$.
$7d = 35 \Rightarrow d = 5$. $a + 45 = 52 \Rightarrow a = 7$. [0.5 Mark]
$a_c = 7 + (c - 1)5 = 5c + 2$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Solving $d = 5, a = 7$: 0.5 Mark
Finding $a_c = 5c + 2$: 0.5 Mark

Correct Answer: $5c + 2$
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