Be a little Gauss

Since

$1 + 2 + 3 + ..... + 99 + 100 = \frac{100 \times 101}{2}$

we can say

$1 + 2 + 3 + ..... + n = \frac{n \times (n + 1)}{2}$

Now, coming to what's asked.

Sum of all positive multiples of 5 that are strictly less than 100 means,

we have to calculate

$5 + 10 + 15 + .... + 95$

$= 5 \times (1 + 2 + 3 + .... 19)$

applying the above formula for $n = 19$ ,

$= 5 \times \frac{19 \times (19 + 1)}{2}$

$= 5 \times \frac{19 \times 20}{2}$

$= 950$

That's the answer!

The positive nos. which are multiples of 5 and strictly less than 100 are 5,10,15...,95. There are 19 such nos.

Now, $(5+10+15+.....+95)+(95+90+85+....+5) = 2\times (Required Sum)$

$\implies (100+100+100+....upto 19 terms) = 2\times (Required Sum)$

$\implies (100\times 19 = 2\times (Required Sum)$

$\implies (Required Sum) = \frac{1900}{2} \implies (Required Sum) =\boxed{950}$

With aritmetics proggesion we have 5 + 10 + 15 + 20 + ... + 95 = 5 ( 1 + 2 + 3 + ... + 19) = 5 x 19 x 20 x 1/2 = 950. Answer : 950.

the multiples of 5 i.e. 5,10,15,.........95 form an A.P. hence its sum can be given by S= n[2a+(n-1)d] /2 where n= no. of terms =19 , a = first term =5 , d = common difference =5 , calculating , we get S=950

5 +10 +15 +20 +25 +30 +35 +40 +45 +50
95 +90 +85 +80 +75 +70 +65 +60 +55

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100 +100 +100 +100 +100 +100 +100 +100 +100 +50 = 950 Or 100 x 19 / 2 = 950

$5+10+15+\cdots+95=5(1+2+3+\cdots+19)=5\times\frac{19\times20}{2}$

95=5*(n-1)5=

90/5=n-1=

18+1=n=

19=n

Sum=(5+95)*N/2=

Sum=(100)*19/2=

Sum=950

5+95=100,90+10=100 so like this we will get such 9 sets+50 so 900+50=950 :-)

Sum of the terms = (N/2)(2a + (N-1)d) ... N=19 .... a= 5 ... d = 5 .. hence sum = 950 !

just add all the multiples of 5 which are less than 100.
they are 5+10+15+20+25+30+35+40+45+50+55+60+65+70+75+80+85+90+95=950.

n/2(1st term +last term) that is n=95-5/5+1=19then 19/2(5+95)=950

it's an arithmetic series where 1st term is a=5,difference between two term is d=5 and total no. of term is n=19 so sum=(n/2) {2 a+(n-1)*d}

5+10+15+20+25+30+35+40+45+50+55+60+65+70+75+80+85+90+95=950

As Gauss did as a little boy, I saw that 5+95=100, 10+90=100, etc. The positive multiples had to be strictly less than 100, so the last number would be 95. When you multiply 100 by 95, you get 950, which is the correct answer. The correct answer is 950.

there are 19 no. of multiplès of 5 from 5 to 95 then for twice 95+5=100 & 100*19/2=950

firstly we want to know how many numbers are there that is multiples of five so the least number multiple of 5 strictly before 100 is 95 so 95/5=19 so we have 19 numbers now we tae the some of the biggest and smallest numbers which are 5 and 95 to be 100 now multbliy the sum with ther numbers divided by 2 ====> 100x19/2=950

The easiest is

105 X 20 : 2 -100 = 950