Question
Download Solution PDFThe sum of the first 2007 terms of the sequence 1, 2, 3, 4, 1, 2, 3, 4, _______ is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFHere, we have repeated series of the first 4 terms i.e. 1,2,3,4 and the sum becomes 10
⇒ Total number of such repeated series = 2004/4 = 501
⇒ Sum of the first 2004 terms = 501 × 10 = 5010
∴ Sum of the first 2007 terms = 5010 + 1 + 2 + 3 = 5016
In this question, We have to find the sum of 1, 2, 3, 4, 1, 2, 3, 4... at 2007-terms. At 2004-terms all four terms (1, 2, 3 and 4) repeat continuously but after 2004 only 1, 2, and 3 occurs for completing 2007 terms. therefore first we have to find the sum of 2004 terms and after we added sum of 1, 2 and 3 in the sum of 2004 terms.
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