Question

how many positive multiples of 10 that are less than 1000 are thesum of 4 consecutive integers

Answer 1

Hi  Yashi

in the question what they given is we have to find the sum of the 4 consecutive numbers their sum should be multiple of  10

ie..10,20.....and should be less than 1000.

so that we can conclude that last 10 multiple before 1000 is 990

then we all know that

1+2+3+4=10

6+7+8+9=30--->20

11+12+13+14=50

16+17+18+19=70

like wise it will be repeated,

based upon the given we need to find upto 990 how many time it occurs.

so  we use this formula to find last number in AP

sn=a+(n-1)d

we knw sn=990=> last number

a=10=> initial number

d=20==>diff between two consecutive numbers

990=10+(n-1)20

990=10+20n-20

990=20n-10

20n=1000

n=50 ans

hope this will bring smile in your face