Question

Find the sum of all natural numbers from $1to200$
i) Which are divisible by $5$
ii) Which are divisible by $3$

Answer 1

i) Numbers divisible by 5 from 1 to 200 are

$5,10,15,......................200$

we can see that, it is AP which has $a=5,d=5$

last term$=200=5+5(n-1)\Rightarrow n=40$

Hence, sum is $\frac{40}{2}[5+200]=20\ast 205=4100$

i) Numbers divisible by 5 from 1 to 198 are

$3,6,9,......................198$

we can see that, it is AP which has $a=3,d=3$

last term$=198=3+3(n-1)\Rightarrow n=66$

Hence, sum is $\frac{66}{2}[3+198]=33\ast 201=6633$