Question

201+202+203+.............300​

Answer 1

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