CAT 2024 Progression Question (Hard)

Question

Consider the sequence , , and t_n left n - 1 right t_ n-2 quad n geq 3. Then, the value of the sum t_2 t_4 t_6 cdots t_ 2024 is

Optima Learn · Accepted Answer

Step 1 Given and for . Step 2 For odd . Hence . These do not appear in the required sum only even indices do . Step 3 For even . With , the product telescopes t_ 2m 2m-1 cdot 2m-3 cdots 3 cdot -1 - 2m-1 . Step 4 Therefore . The sum t_2 t_4 cdots t_ 2024 - sum_ m 1 1012 2m-1 - ,1012 2. Step 5 Compute

CAT 2024 Progression — Previous Year Question

CAT 2024

Quantitative

Progression

Hard

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