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प्रश्न
Find the sum of all multiples of 7 lying between 500 and 900.
उत्तर
The multiples of 7 lying between 500 and 900 are 504, 511, 518, … , 896.
This is an A.P.
First term, a = 504
Common difference, d = 511 − 504 = 7
Last term = 896
Let there be n terms in the A.P.
`a_n=896`
`rArr a+(n+1)d=896`
`rArr 504+(n-1)xx7=896`
`rArr (n-1)xx7=896-504`
`rArr (n-1)=392/7`
`rArr n-1=56`
`rArr n=57`
We know that, `S_n=n/2(a+l)`
∴Sum of all the multiples of 7 lying between 500 and 900
`=57/2(504+896)`
`=57/2xx1400`
`=57xx700`
`=39900`
Thus, the sum of all the multiples of 7 lying between 500 and 900 is 39900.
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