Question

Find the sum of all the numbers between 500 and 800 divisible by 8.

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{The sum of all the numbers between 500 and 800}$

$\textsf{divisible by 8}$

$\underline{\textsf{Solution:}}$

$\textsf{The numbers divisible by 8 are}$

$\mathsf{504,512,520,..........,792}$

$\mathsf{This\;is\;an\;A.P\;with\;a=504\;and\;d=8}$

$\mathsf{Number\;of\;terms\;in\;the\;A.P}$

$\boxed{\mathsf{n=\dfrac{l-a}{d}+1}}$

$\mathsf{n=\dfrac{792-504}{8}+1}$

$\mathsf{n=\dfrac{288}{8}+1}$

$\mathsf{n=36+1}$

$\implies\mathsf{n=37}$

$\mathsf{Now}$

$\textsf{Sum of all the numbers between 500 and 800}$

$\mathsf{S_n=\dfrac{n}{2}[a+l]}$

$\mathsf{S_{37}=\dfrac{37}{2}[504+792]}$

$\mathsf{S_{37}=\dfrac{37}{2}[1296]}$

$\mathsf{S_{37}=37{\times}648}$

$\implies\boxed{\mathsf{S_{37}=23976}}$

$\underline{\textsf{Find more:}}$

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Answer 2

Given :- Find the sum of all the numbers between 500 and 800 divisible by 8. ?

Solution :-

Between 500 and 800 :-

• First term divisible by 8 = 504 = a .
• second term = 512
• third term = 520
• last term = 792 .

So, we can conclude that,

• 504, 512 , 520 _____________ 792 is an AP series .

whose ,

• first term = 504
• common difference = 8
• Last term = 792 .

we know that,

• nth term of an AP = a + (n - 1)d .

So,

→ 792 = 504 + (n - 1)8

→ 792 = 504 + 8n - 8

→ 792 = 496 + 8n

→ 8n = 792 - 496

→ 8n = 296

→ n = 37 .

Therefore,

→ Sn = (n/2)[ first term + Last term]

→ Sn = (37/2)[ 504 + 792 ]

→ Sn = (37/2) * 1296

→ Sn = 37 * 648

→ Sn = 23,976 (Ans.)

Hence, the sum of all the numbers between 500 and 800 divisible by 8 is 23,976.

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