Progressions : Sum of terms of an Arithmetic Sequences

Question

The sum of 20 terms of the series -1² + 2² - 3² + 4² - 5² + 6².... is:

1. 210
2. 519
3. 190
4. 420
   
   

Correct Choice is (1) and Correct Answer is 210

Explanatory Answer

-1² + 2² - 3² + 4² - 5² + 6².... upto 20 terms can be written as

(-1² + 2²) + (-3² + 4²) + (-5² + 6²) + ..... upto 20 terms.

= (-1 + 2) (1 + 2) + (-3 + 4) (3 + 4) + (-5 + 6) (5 + 6) +..... (-19 + 20) (19 + 20)

= (1 + 2) + (3 + 4) + (5 + 6) + ..... + (19 + 20)

Sum of the first 'n' natural numbers =

Therefore, sum of the given series = = 210.

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