Question

Find the sum of all numbers between 400 and 600 , which are divisible by 9

Answer 1

Answer:

Sum of all numbers b/w 400 and 600 divisible by 9 is

10989

Step-by-step explanation:

Numbers b/w 400 and 600 divisible by 9 are :

405 , 414 , 423 ........ 594 .

As we can see ,

these numbers are forming an AP

( AP is defined as as sequence of numbers with difference between their consecutive terms remaining constant )

so,

→ first term of AP , a = 405

→ common difference, d = 414 - 405 = 9

→ last term of AP , l = 594

Let, there are n terms in this AP

then,

↦ aₙ = a + ( n - 1 ) d

↦ l = a + ( n - 1 ) d

↦ 594 = 405 + ( n - 1 ) ( 9 )

↦ 594 - 405 = 9 n - 9

↦ 189 = 9 n - 9

↦ 9 n = 189 + 9

↦ 9 n = 198

↦ n = 198 / 9

↦ n = 22

Now,

finding the sum of all numbers between 400 and 600 divisible by 9

↦ Sₙ = n ( a + aₙ ) / 2

↦ Sₙ = n ( a + l ) / 2

↦ S₂₂ = 22 ( 405 + 594 ) / 2

↦ S₂₂ = 11 ( 999 )

↦ S₂₂ = 10989

Hence, the sum of all numbers between 400 and 600 divisible by 9 is 10989 .