Aptitude - Numbers - Discussion

1) tn = a+(n-1)d --> [ a=first term, n=no. of terms, d=difference between terms, tn=last term ]
tn = 6+(n-1)6
tn = 6+6n-6
tn = 6n

2) sn = n/2(a+l) -----------------> [ sn=sum, n=no. of terms, a=first term, l=last term ]
1800 = n/2(6+tn) ------------> [ l=tn from (1) ]
3600 = n(6+6n),
600 = n(1+n),
600 = n+n^2,
n^2+n-600 = 0.
n^2+25n-24n-600 = 0,
n(n+25)-24(n+25) = 0,
(n+25)(n-24) = 0,
n=-25 or n=24.
n=24 ---------> [ consider positive value].

So, the answer is 24.

@All.

This method will clear your doubt.

6+12+18...... = 1800
6(1+2+3+....) = 1800
1+2+3 = 300.
so, n(n+1)/2 = 300 (this is the formula to calculate the sum of the natural number since 1+2+3+....series is a natural number series.

n(n+1) = 600.
Now think what could be n.
24^576
25^625 since(n+1)

Now,
n(n+1) = n^2+n,
take n = 24^2,
so 24^2 + 25 = 600,
25 = 600 - 24^2 = 24 so the answer is 24.

In the previous problem we know the last term. If we know the last term we can use the formula [a+(n-1)d] = L(last term) then we can find the number of terms n and we can calculate sum of terms using n/2(a+l).

But in above case we know the sum of terms is 1800 so using sum of n terms formula n/2[2a+(n-1)d] we will calculate the number of terms.

1800 = n/2[2a+(n-1)d],
1800 = n/2[2*6+(n-1)6],
3600 = n[12+6n-6],
3600 = n[6n+6],
6n^2+6n-3600 = 0,
6(n^2+n-600) = 0,
n^2+n-600 = 0,
n^2+25n-24n-600 = 0,
n(n+25)-24(n+25) = 0,
(n+25)(n-24) = 0,
n=-25 , n = 24,
Negative value is not valid.
Therefore, n=24.

How you get 3n(n+1) = 1800?

Solution is;
n/2 [2 x 6 + (n - 1) x 6] = 1800,
n/2 [12 + (6n-6)] = 1800,
12n/2 + 6n2/2 - 6n/2=1800,
12n+6n2-6n/2=1800,
6(2n+1n2+1n)/2=1800,
6(1n2+1n)/2=1800,
3(1n2+1n)=1800,
3n(n+1)=1800.

Please tell me why we have taken this formula, i.e n/2[2a+(n-1)]d.

In the previous problem of (2+4+6+...30) we have taken the formula as [a+(n-1)d]. So tell me which formula must be used for which problem.

(6+6x)x/2 = 1800.
(6+6x)x = 3600,
6x^2+6x-3600 = 0,
6(x^2+x-600) = 0,
x^2+x-600 = 0,
x^2+25x-24x-600 = 0,
x(x+25)-24(x+25) = 0,
(x-24) or (x+25).
x=24 or x= -25.

So ans n=24.

Please explain me how could it become as n (n+1) = 600.

From this step to last step I did not understood please anyone help me to know.

Another method:

6+12+...... = 1800,

6(1 + 2 + 3 + ....) = 1800,

1+2+3.... = 300,

So, n(n+1)/2 = 300,

n(n+1) = 600.

Please explain me step 3rd.

How you get 3n (n+1) = 1800?