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Find the sum of all multiples …

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Find the sum of all multiples of 7 lying between 500 to 900

Posted by Pratham Ratan 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

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 {tex}\Rightarrow{/tex} a + (n - 1)d = 896 {tex}\Rightarrow{/tex}504 + (n -1) {tex}\times{/tex} 7 = 896 {tex}\Rightarrow{/tex}497 + 7n = 896
{tex}\Rightarrow{/tex}7n = 399 {tex}\Rightarrow{/tex}n = 57.
{tex}\therefore{/tex}required sum = {tex}\frac{n}{2}{/tex}(a + l)
={tex}\frac{{57}}{2}{/tex}{tex}\cdot{/tex}(504 + 896) = ({tex}\frac{{57}}{2}{/tex}{tex}\times{/tex}1400) = 39900.
Hence, the required sum is 39900.

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CBSE > Class 10 > Mathematics