Question

find the sum of all multiples of 7 lie between 500 and 900

Answer 1

Hi ,

504 , 511 , 518 , ....,889, 896 are

multiples of 7 between 500 and 900

and these are in Arithmetic

progression .

First term = a = 504 ,

Common difference = a2 - a1

d = 511 - 504 = 7

Let the number of terms = n

Last term ( L ) = 896

We know that ,

a + ( n - 1 )d = L

504 + ( n - 1 ) 7 = 896

Divide each term with 7 , we get

72 + n - 1 = 128

71 + n = 128

n = 128 - 71

n = 57

Therefore ,

*****************************************

Sum of n terms ( Sn )= n/2 [ a + L ]

****************************************

Sum of the 57 terms = S57


S57 = (57/2 )[ 504 + 896 ]

=( 57/2 ) [ 1400 ]

= 57 × 700

= 39900

Sum of 7 multiples between 500 and

900 = 39900

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!




Thanks