Permutations and Combinations

Permutations and Combinations

Question

Find the sum of all natural numbers lying between 100 and 1000, which are mutliples of 5.

Answer

All the natural numbers between 100 and 1000 which are multiples of 5 are:
105, 110, 115, ......, 995.
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Here, a = 105,  d = 110 - 105 = 5, straight t subscript straight n space equals space 995.
i.e.,      a + (n - 1)d = 995           or             105 + (n - 1)5 = 995
or            5n + 100 = 995             or             5n = 995 - 100 = 895
or           space space straight n equals space 895 over 5 space equals space 179

∴                     straight S subscript 179 space equals space 179 over 2 left square bracket 105 space plus space 995 right square bracket space left square bracket because straight S subscript straight n space equals space straight n over 2 left parenthesis straight a space plus space straight l right parenthesis right square bracket
                              equals 179 over 2 space left parenthesis 1100 right parenthesis space equals space 179 space cross times space 550 space equals space 98450.

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