1.

Find the sum of all multiples of 7 lying between 500 and 900.

Answer» All multiples of 7 lying between 500 and 900 are
504, 511, 518, …, 896
This is an AP in which a = 504, d = 7 and l = 896.
Let the given AP contain n terms. Then,
`T_(n) = 896 rArr a+ (n-1)d = 896 rArr 504 + (n-1) xx 7 = 896`
`rArr 497 + 7n = 896 rArr 7n = 399 rArr n = 57.`
`therefore "required sum" = (n)/(2) (a+l)`
` = (57)/(2) *(504 + 896) = ((57)/(2) xx 1400)` = 39900.`
Hence, the required sum is 39900.


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