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# 10 + 11 + 12 +...+ x = 5106 What is x?

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Re: 10 + 11 + 12 +...+ x = 5106 What is x? [#permalink]
Sum of first x natural number = x(x+1)/2 = 5106+45
Where 45 is the sum of the first 9 numbers (which is missing in the series)

X(X+1) = 10302

must be 101,102 or 103,104 (last digit is 2)
quickly solving the pairs helps to identify the answer
x = 101
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Re: 10 + 11 + 12 +...+ x = 5106 What is x? [#permalink]
We have a direct formula for sum of n terms in Arithmetic progression.
Sum of n terms= (n/2)*(2a+(n-1)d)

Where n is the number of terms in A.P
"a" is the first term in the series
"d" common difference between two consecutive terms.

No add 1-9 numbers on both sides so we get a new arithmetic series as 1+2+3+4+...+x =5151

Upon substituting the above values and making it equal to 5151 leaves the answer as x=101
(a=1, d=1, Sum =5151)

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Re: 10 + 11 + 12 +...+ x = 5106 What is x? [#permalink]
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