201+202+203+.............300
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Sum of Arithmetic Series
Given : 200 + 201 + .......... + 300
To find : the sum
Solution :
- Here the given arithmetic series is
- 200 + 201 + .......... + 300
- The first term is 200, the common difference is 1 and the nth term (say) is 300
- Since 300 is the nth term, we can write:
- 200 + (n - 1) × 1 = 300
- or, 200 + n - 1 = 300
- or, n = 101
- So there are 101 terms in the given Arithmetic series
- Thus the sum of 101 numbers in the given series is
- = 101/2 * (first term + last term)
- = 101/2 * (200 + 300)
- = 101/2 * 500
- = 101 * 250
- = 25250
Answer : 200 + 201 + .......... + 300 = 25250
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