I found this question in the difficult list of the quant questions, but not able to figure out how this is to be solved. Looks very simple though:
The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
Maths Question
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If you mean consecutive even numbers between 1 and n, we can solve it the following way:
let us express the terms in the sum as 2X_i as they are all even. X_i are consecutive #s.
Sum(2X_i) for i=1 to n is 79*80.
This implies:
2 * Sum(X_i) (for i=1 to n) = 79*80.
Since X_i are consecutive, Sum(X_i)(for i=1 to n) = n(n=1)/2.
So, 2 * n(n+1)/2 = 79*80 => n(n+1) = 79*80 => n = 79.
indeed sum{2, 4, 6 ... 158} (where there are n=79 terms) = 79*80.
let us express the terms in the sum as 2X_i as they are all even. X_i are consecutive #s.
Sum(2X_i) for i=1 to n is 79*80.
This implies:
2 * Sum(X_i) (for i=1 to n) = 79*80.
Since X_i are consecutive, Sum(X_i)(for i=1 to n) = n(n=1)/2.
So, 2 * n(n+1)/2 = 79*80 => n(n+1) = 79*80 => n = 79.
indeed sum{2, 4, 6 ... 158} (where there are n=79 terms) = 79*80.
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When you say sum is for numbers between 2 to 158, it is not possible that these numbers are between 1 and 79 as mentioned in the question itself.
Suppose n=9, numbers we are concerned with are
2, 4, 6, 8
But 2 + 4 + 6 + 8 NOT = 2(1+2+....+9) as you indicated.
It will be 2(1+2+3..+(n-1/2))
Correct me if I am wrong.
Suppose n=9, numbers we are concerned with are
2, 4, 6, 8
But 2 + 4 + 6 + 8 NOT = 2(1+2+....+9) as you indicated.
It will be 2(1+2+3..+(n-1/2))
Correct me if I am wrong.
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first even number=2
last even number=n-1
total number of even numbers= (n-1-2)/2 + 1= n/2-3/2+1
=(n-1)/2
sum of A.P =total number/2(first term + last term)
in our case
(n-1)/4 * (2+n-1)=79*80
(n-1)(n+1)=4*79*80= 158*160
n=159
last even number=n-1
total number of even numbers= (n-1-2)/2 + 1= n/2-3/2+1
=(n-1)/2
sum of A.P =total number/2(first term + last term)
in our case
(n-1)/4 * (2+n-1)=79*80
(n-1)(n+1)=4*79*80= 158*160
n=159
The powers of two are bloody impolite!!