Four

What is the sum of all numbers from 1 to 100 that are divisible by 4?

1360 1440 1204 1300

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1 solution

Pham Khanh
Apr 20, 2016

T h e s u m t h a t w e n e e d t o c o u n t i s : The~sum~that~we~need~to~count~is: S = n = 1 25 4 n = 4 + 8 + + 100 S=\displaystyle \sum_{n=1}^{25} 4n=4+8+\cdot\cdot\cdot+100 T h e s u m i s g i v e n b y : The~sum~is~given~by: ( f i r s t n u m b e r + l a s t n u m b e r ) × a m o u n t o f n u m b e r s 2 \frac{(first~number+last~number) \times amount~of~numbers}{2} A n d t h e a m o u n t o f n u m b e r s S i s : And~the~amount~of~numbers \in S~is: 100 4 4 + 1 = 96 4 + 1 = 24 + 1 = 25 \frac{100-4}{4}+1=\frac{96}{4}+1=24+1=25 S o : So: S = ( 100 + 4 ) × 25 2 = 2 × ( 50 + 2 ) × 25 2 = ( 50 + 2 ) × 25 = 52 × 25 = 1300 S=\frac{(100+4) \times 25}{2}=\frac{2 \times (50+2) \times 25}{2}=(50+2) \times 25=52 \times 25=1300 H e n c e , t h e a n s w e r i s : Hence,~the~answer~is: 1300 \huge \color{#EC7300}{\boxed{\color{#D61F06}{1300}}}

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