Question

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

Answer 1

Step-by-step explanation:

Let the numbers be 3,9,15,21...........999

Let be (a1)=3

and d=6

Put 999 in place of a(n)

Use this formula :-

=>a(n)= (a1)+(n-1)×d

=>(999) =3+(n-1)×6 

=>996/6 =n-1 

=>166=n-1

=>n=166+1

=>n=167 terms 

Now we are find the value n Now start with the 1st term a(1)=3 and (n) = 167 and last term is a(n) =999.

S(n) = n/2×{ a(1) + a(n) }

S(n) = 167/2×[3+999] 

S(n) = (167/2)×(1002)

S(n)= 167×501 

Hopes it help you❤️❤️

S(n) = 83,667