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Find the sum of those integers numbers between 1and 500 divisible by 2 and 5

Answer»

Answer: 12250

Hope this helps!

Step-by-step explanation: integers which are multiples of 10 are also the multiples of 2 and 5.

Therefore, multiples of 2 as well as of 5 between 1 and 500 are:

10, 20, 30, ...., 490 

Series forms an AP with first term,a=10 and common difference,d=20-10=10.

Let total number of TERMS of this AP be n.

Therefore, NTH term of AP, an = Last term, l= 490 

an=a(n-1)d=l;

10+(n-1)10=490;

(n-1)10=480;

n-1=48;

n=48+1=49;

n=49

Thus,sum of n terms of AP is given as:

S₄₉=49/2 (10+490);

     =49/2 (500);

     =49×250=12250


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