mark7143 mark7143
  • 06-10-2018
  • Mathematics
contestada

Find the sum of all the multiples of 7 in between of 1 and 100

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jimrgrant1 jimrgrant1
  • 06-10-2018

735

the multiple of 7 are 7, 14, 21, ...., 98 ( n = 14 )

this is an arithmetic sequence and the sum to n terms is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1 )d ]

d = 14 - 7 = 21 - 14 = 7 and a = 7

[tex]S_{14}[/tex] = 7 [ ( 2 × 7 ) + (13 × 7 ) ] = 7 ( 14 + 91 ) = 735


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