Question

find the sum of all integers between 100 and 550 which are divisible by 9

Answer 1

Answer:

The sum of all integers between 100 and 550, which are divisible by 9 is 16425.

Step-by-step explanation:

Integers between 100 and 550, which are divisible by 9 are  108, 117, 126 , ....... 549

Here,  

a = 108, d = 9, an(l) = 549

By using the formula ,an = a + (n - 1)d

549 = 108 + (n -1)9

549 - 108 =  9(n -1)

441 = 9(n -1)

n -1 = 441/9

n -1 = 49

n = 49 + 1  

n = 50

By using the formula ,Sum of nth terms , Sn = n/2 [a + l]

⇒ S50 = 50/2 (a + l)

⇒ S50 = 25 (108 + 549)

⇒ S50 = 25 × 657

⇒ S50 = 16425

Hence, the sum of all integers between 100 and 550, which are divisible by 9 is 16425.

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Answer 2

Answer:

The sum of all integers between 100-550 and also they must be divisible by 9 are :-

From 108,117..........549

Now here,

a = 108

d = 9

I = 549

By using the formula :-

I = a+(n-1)d

549 = 108+(n-1)9

549 - 108 = (n-1)9

(n-1)= (441)9

n-1 = 49

n = 50

We found n = 50

Now By using the formula to find the sum of nth term

Sn = n/2 [ a + I ]

50S = 50/2[108+549]

50S = 25 × 657

S = 16425

Hence , the sum of All integers between 100-550 which are divisible by 9 is 16425.

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