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given 1,2,3,4,5,....49 consecutive numbers
x is the number such that
sum of preceding numbers of x = sum of following numbers of x
sum of ( 1,2,3,....x-1) = sum of [(x+1), (x+2) ,....48,49]
(x-1)/2[1+x-1] =(49-x)/2[x+1+49]
(x-1)x=(49-x)(x+50)
x²-x=49x+2450-x²-50x
x²-x =2450-x²-x
x²+x²-x+x=2450
2x²=2450
x²=2450/2
x²=1225
x=√1225
x=35
required number is x= 35
sum of (1,2,3.....34) = sum of (36,37,....49
OR
The total number of houses preceding the house numbered x = (x-1)
and the number of housed following the house numbered x = 49-x
The house number following the house number x = x+1
According to quesiton
Sx-1 = S4 9-x
For the house preceding house number x:a = 1, d = 1, n = x-1
For the house following house number x:a = x+1, d = 1, last term, l = 49
So,
[(x-1)/2][2(1)+(x-1-1)(1)} = [(49-x)/2][(x+1)+49]
[(x-1)/2]92+x-2) = [(49-x)/2](50+x)
(x-1)(x) = (49-x)(50+x)
x2 - x = 2450 + 49x - 50x - x2
x2 - x = 2450 - x - x2
x2 - x + x + x2 = 2450
2x2 = 2450
x2 = 2450/2 = 1225
x = sqrt(1225)
x = 35
H҉ O҉ P҉ E҉ I҉ T҉ H҉ E҉ L҉ P҉ S҉ Y҉ O҉ U҉
x is the number such that
sum of preceding numbers of x = sum of following numbers of x
sum of ( 1,2,3,....x-1) = sum of [(x+1), (x+2) ,....48,49]
(x-1)/2[1+x-1] =(49-x)/2[x+1+49]
(x-1)x=(49-x)(x+50)
x²-x=49x+2450-x²-50x
x²-x =2450-x²-x
x²+x²-x+x=2450
2x²=2450
x²=2450/2
x²=1225
x=√1225
x=35
required number is x= 35
sum of (1,2,3.....34) = sum of (36,37,....49
OR
The total number of houses preceding the house numbered x = (x-1)
and the number of housed following the house numbered x = 49-x
The house number following the house number x = x+1
According to quesiton
Sx-1 = S4 9-x
For the house preceding house number x:a = 1, d = 1, n = x-1
For the house following house number x:a = x+1, d = 1, last term, l = 49
So,
[(x-1)/2][2(1)+(x-1-1)(1)} = [(49-x)/2][(x+1)+49]
[(x-1)/2]92+x-2) = [(49-x)/2](50+x)
(x-1)(x) = (49-x)(50+x)
x2 - x = 2450 + 49x - 50x - x2
x2 - x = 2450 - x - x2
x2 - x + x + x2 = 2450
2x2 = 2450
x2 = 2450/2 = 1225
x = sqrt(1225)
x = 35
H҉ O҉ P҉ E҉ I҉ T҉ H҉ E҉ L҉ P҉ S҉ Y҉ O҉ U҉
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