


Method and examples


Arithmetic Progression 



Problem 13 of 19 


13. Find the sum of all natural nos between to and which are not divisible by .










Solution 
Solution provided by AtoZmath.com


Want to know about

This is demo example. Please click on Find button and solution will be displayed in Solution tab (step by step)
Arithmetic Progression 
13. Find the sum of all natural nos between 100 to 200 and which are not divisible by 4 .
Required Addition = `(100 + 101 + 102... + 200)  (100 + 104 + 108... + 200)`
Required Addition = `S'  S''`
We know that, `S_n = n/2 (a + l)`
`:. S_101 = 101/2 * (100 + 200)`
`= 101/2 (300)`
`= 15150`
Numbers between `100` and `200` divisible by `4` are `100, 104, 108 ...`
Which are in arithmetic progression. In which `a=100` and `d=4`
Let `n` be the term such that `f(n) = 200`
We know that, `f(n) = a + (n  1)d`
`100 + (n  1)(4) = 200`
`(n  1)(4) = 100`
`n  1 = 25`
`n = 26`
We know that, `S_n = n/2 [2a + (n  1)d]`
`:. S_26 = 26/2 * [2(100) + (26  1)(4)]`
`= 13 * [200 + (100)]`
`= 13 * [300]`
`= 3900`
`:.` Required Addition = `15150  3900`
`= 11250`







