Suppose we have an arithmetic progression a₁, a₂, ldots aₙ, ldots with a₁=1, a₂-a₁=5 . m

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8. Sequences and Series

hard

Suppose we have an arithmetic progression $a_1, a_2, \ldots a_n, \ldots$ with $a_1=1, a_2-a_1=5$. The median of the finite sequence $a_1, a_2, \ldots, a_k$, where $a_k \leq 2021$ and $a_{k+1} > 2021$ is

A

$1011$

B

$1011.5$

C

$1013.5$

D

$1016$

(KVPY-2021)

Solution

(a)

$a_1, a_2, a_3, \ldots a_n$ are in A.P.

$a_1=2, a_2-a_1=5=d$

$a_k \leq 2021$

$a_1+(k-1) d \leq 2021$

$k \leq 405$

median of $a_1, a_2, \ldots, a_{405}$

is $a_{203}=a_1+(203-1) d=1011$

Standard 11

Mathematics

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