Sequence And Series

Step 1: Identifying the Pattern The sequence consists of alternating even and odd terms: Grouping them: - The even-indexed terms form: - The odd-indexed terms form:
Step 2: Sum of Even-Indexed Terms This sequence follows an arithmetic progression with: The sum of the first terms of an AP is: Substituting values:
Step 3: Sum of Odd-Indexed Terms For the sequence , with and , using the same sum formula:
Step 4: Total Sum of the Sequence Adding both: Thus, the required sum is: