Multiple choice

What shall be the sum of the first 2007 terms of the series given below :1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, ........

  1. 5016

  2. 5024

  3. 5038

  4. 5052

  5. 5116
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A Correct answer
Explanation

The series repeats every 4 terms (1, 2, 3, 4). The sum of one cycle is 10. 2007 divided by 4 is 501 with a remainder of 3. The sum is 501 * 10 + (1 + 2 + 3) = 5010 + 6 = 5016.

AI explanation

The given series repeats the block 1, 2, 3, 4, which sums to 10. Dividing 2007 by 4 yields 501 full blocks with a remainder of 3 terms. The sum of the 501 full blocks is 5010, and the sum of the remaining three terms is 1 + 2 + 3 = 6. Adding these together gives 5010 + 6 = 5016.

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