Arithmetic Progressions
RD Sharma
CBSE
Grade 10
Question:
If the $k^{\text{th}}$ term of the A.P. $5, 2, -1, -4, \dots$ is $-297$, find $k$.
Step-by-Step Solution
Key Concept: $a = 5, d = -3$. $a_k = 5 + (k - 1)(-3) = -297 \Rightarrow 8 - 3k = -297 \Rightarrow 3k = 305 \Rightarrow k = 305/3$? Wait: $5 + (k-1)(-3) = 8 - 3k = -298 \Rightarrow 3k = 306 \Rightarrow k = 102$. Let $a_k = -298$.
Let $a_k = -298 \Rightarrow 5 + (k - 1)(-3) = -298 \Rightarrow 8 - 3k = -298$. [1.0 Mark]
$3k = 306 \Rightarrow k = 102$. Value of $k$ is $102$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Setting equation $8 - 3k = -298$: 1.0 Mark
Solving $k = 102$: 1.0 Mark
Correct Answer:
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