Saved Bookmarks
| 1. |
Find the sum of all multiples of 7 lying between 500 to 900 |
| Answer» All multiples of 7 lying between 500 and 900 are504,511,518,...,896This is an AP in which a = 504, d=7 and l = 896.Let the given AP contain n terms. Then,Tn = 896\xa0{tex}\\Rightarrow{/tex} a + (n\xa0- 1)d = 896 {tex}\\Rightarrow{/tex}504 + (n -1) {tex}\\times{/tex}\xa07 = 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. | |