Question

The houses of a row are numbered consicutively from 1 to 49 show that there is a Value of m such that The sum of Number of the houses preeceding the house marked m is equal to the sum of numbers of the houses following it . FIND THIS VALUE OF M

Answer 1

Answer:

let Sm-1 be the sum of number of  houses preceding mth house

Sm be the sum of all number of  houses including and upto mth house

then

Given that Sm-1 =S49-Sm      ....(a), a=1 ,d=1

using Sn = n/2(2a+(n-1)d)

Sm =[m/2](2+(m-1))= m(m+1)/2   ....(b)

Sm-1 = [(m-1)/2](2+(m-2)) = (m-1)m/2   .....(c)

S49 = 49/2(2+48) = 49*25 = 1225   ....(d)

substituiting b, c, d in a

(m-1)m/2 = 1225 - m(m+1)/2

=> ($m^{2}$  -m)/2 + ($m^{2}$ + m)/2 = 1225

=> 2 *$m^{2}$= 1225 *2

=>m = 35

Step-by-step explanation: