Question

sum of all odd numbers between 1 and 1000 which are divisible by 3 is​

Answer 1

Answer:

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667

Step-by-step explanation:

divisible by 3, are

3,9,15,......999

which forms an A.P

first term of this A.P is a1=3

second term of this A.P is a2=9

last term of this A.P is an=999

common difference 

d=a2−a1

⟹d=9−3=6 .

nth term of this A.P is given by

an=a1+(n−1)d

put an=999;a1=3 and d=6 in above equation we get,

⟹999=3+(n−1)6

⟹6n−6+3=999

⟹6n=999+3=1002

n=61002=167 number of terms in this A.P

now, sum of these n=167 terms is given by

Sn=2n(a1+an)

put values of n=167;a1=3;an=999 we get

S167 =2167(3+999)

⟹S167=2167×1002

⟹S167=167×501

⟹S167=83667

hence the sum of all odd numbers between 1 and  1000 which are divisible by 3, is S167=83667