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The first 24 terms of an arithmetic series are: $35+42+49+...+196$. Calculate the sum of ALL natural numbers from 35 to 196 that are not divisible by 7
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Sum of multiples of 7 from 35 to 196:

$a=35, d=7$

$S_{n}=\frac{n}{2}[a+l]$

$= \frac{24}{2}[35 + 196]$

$ = 12[231]$

=2772

Sum of all natural numbers from 35 to 196

$a=35, d=1, n=162$

$S_{n} = \frac{n}{2}[a+l]$

$ = 81[231]$

$ = 18 711$

 

Therefore Sum of all numbers not divisible by 7:

$ = 18711 - 2772 $

$ = 15 939$
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