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Jee Main 2025 — Medium JEE math MCQ

Let \(\{a_n\}\) be a sequence such that \(a_0 = 0, a_1 = \frac{1}{2}\) and \(2a_{n+2} = 5a_{n+1} - 3a_n, n = 0, 1, 2, 3, \ldots\). Then \(\sum_{k=1}^{100} a_k\) is equal to
  1. A. \( 3a_{99} - 100 \)
  2. B. \( 3a_{100} + 100 \)
  3. C. \( 3a_{99} + 100 \)
  4. D. \( 3a_{100} - 100 \)

Solution

The correct option is **B**. (B. \( 3a_{100} + 100 \))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let {an}\{a_n\} be a sequence such that a0=0,a1=12a_0 = 0, a_1 = \frac{1}{2} and 2an+2=5an+1−3an,n=0,1,2,3,…2a_{n+2} = 5a_{n+1} - 3a_n, n = 0, 1, 2, 3, \ldots. Then ∑k=1100ak\sum_{k=1}^{100} a_k is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep