Permutations and Combinations

Permutations and Combinations

Question

Find the sum of all the numbers between 200 and 400 which are divisible by 7.

Answer

All the numbers between 200 and 400, which are divisible by 7 are:
              203, 210, 217 ......, 399.
Here, a = 203, d = 210 - 203 = 7, straight t subscript straight n space equals space 399.
or                 a + (n - 1)d = 399
                  203 + (n - 1) 7 = 399
rightwards double arrow                     (n - 1) 7 = 399 - 203 = 196 space rightwards double arrow space space space space space space space space space space space space straight n space minus space 1 space equals space 196 over 7 space equals space 28 space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space space space space space straight n space equals space 29

∴                           straight S subscript 29 space equals space 29 over 2 space left square bracket space 203 space plus space 399 right square bracket space equals space 29 over 2 space cross times space 602           [Use straight S subscript straight n space equals space straight n over 2 left parenthesis straight a plus space straight l right parenthesis]
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