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Sequences and Series question

2025 · 28 Jan · Shift 1 · Q30

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JEE Main
Mathematics
Sequences and Series
2025 · 28 Jan · Shift 1 · Q30

Sequences and Series question

2025 · 28 Jan · Shift 1 · Q30

JEE MainMathematicsSequences and SeriesMCQ+4 / −1

Let

\left\langle a_{\mathrm{n}}\right\rangle

be a sequence such that

a_0=0, a_1=\frac{1}{2}

and

2 a_{\mathrm{n}+2}=5 a_{\mathrm{n}+1}-3 a_{\mathrm{n}}, \mathrm{n}=0,1,2,3, \ldots

. Then

\sum\limits_{k=1}^{100} a_k

is equal to

A
$3 a_{100}+100$
B
$3 a_{100}-100$
C
$3 a_{99}-100$
D
$3 a_{99}+100$

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