JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

Let the sequence,

{a_1},{a_2},{a_3}, \ldots ,\;{a_{2n}},

form an AP, then

a_1^2 - a_2^2 + a_3^2 - ... + a_{2n - 1}^2 - a_{2n}^2

is equal to

View answer and explanation

Correct option: A

\frac{n}{{2n - 1}}\left( {a_1^2 - a_{2n}^2} \right)

Option A is correct because the given expression can be simplified using the properties of arithmetic progressions and factorization.

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