@bullseyes said:300! is divisible by (24!)^n.Max. possible integral value of n ?
13
@deedeedudu said:13
@ScareCrow28 said:Power of 23.. 13
@FoolNFinal said:13....@maneeshp ... maine kuch galti kar di accidently mere ans sahi ho gaya..w8 dekhata hu..
13 is correct
What is the sum of the first 20 terms of the series :
48, 100, 180, 294, 448...
a)63710 b)71630 c)73610 d)None
@ron123
this is not a soln....
its not even the differences that are in AP....it is diff of diff that are in AP.....and it involves big numbers......calculation can become quite lengthy.....
so if i get this question in the exam, i would leave it...(unless i have loads of time, which generally isn't the case with IIFT)
this is not a soln....
its not even the differences that are in AP....it is diff of diff that are in AP.....and it involves big numbers......calculation can become quite lengthy.....
so if i get this question in the exam, i would leave it...(unless i have loads of time, which generally isn't the case with IIFT)
@shadowwarrior said:@ron123this is not a soln....its not even the differences that are in AP....it is diff of diff that are in AP.....and it involves big numbers......calculation can become quite lengthy.....so if i get this question in the exam, i would leave it...(unless i have loads of time, which generally isn't the case with IIFT)
I already left this in mocks... 
Was looking for some shortcut way for this.....
Was looking for some shortcut way for this.....@ron123 said:What is the sum of the first 20 terms of the series : 48, 100, 180, 294, 448...a)63710 b)71630 c)73610 d)None
general term is 2*[7n^2+5n+12]
sum : 42760 ... none
@grkkrg said:how did you get this?
assume eq ax^2+bx+c
for n=1.... a+b+c = 48
for n=2... 4a+2b+c=100
for n=3... 9a+3b+c = 180
solve 3 eq.. get a,b,c
@FoolNFinal said:assume eq ax^2+bx+cfor n=1.... a+b+c = 48for n=2... 4a+2b+c=100for n=3... 9a+3b+c = 180solve 3 eq.. get a,b,c
Good one .... :)
@FoolNFinal said:assume eq ax^2+bx+cfor n=1.... a+b+c = 48for n=2... 4a+2b+c=100for n=3... 9a+3b+c = 180solve 3 eq.. get a,b,c
@ron123 said:Good one ....
:thumbsup:
Adding some useful information on your solution:
The formula you've used here is a special case. We cannot apply it on every problem.
In this problem, given series is 48, 100, 180, 294, 448........
Differences between the two terms are 52, 80, 114, 154.....
Differences of differences between the two terms in the series are 28, 34, 40...
==> An A.P. (Common difference is 6)
==> nth term will be of A*n^3+B*n^2+C*n+D type.
If in any other series, differences are in A.P.,
then nth term =A*n^2+B*n+C
If differences of differences of differences are in A.P.,
then nth term = A*n^4+B*n^3+C*n^2+D*n+E
And so on 😃 
@ron123 said:What is the sum of the first 20 terms of the series : 48, 100, 180, 294, 448...a)63710 b)71630 c)73610 d)None
48,100, 180, 294, 448
1st difference: 52, 80, 114, 154
2nd difference: 28, 34, 40
3rd difference: 6,6
we see that third difference is constant hence general term must be a cubic
using successive difference (not solving any eqn here!) we can find the coefficients to
n^3+8n^2 + 21n + 18
=(n+2)(n+3)^2
hence sum upto 20 terms = 71830
Hence none of these.
ATDH.
@vijay_chandola said:Adding some useful information on your solution:The formula you've used here is a special case. We cannot apply it on every problem.In this problem, given series is 48, 100, 180, 294, 448........Differences between the two terms are 52, 80, 114, 154.....Differences of differences between the two terms in the series are 38, 34, 30...==> An A.P. (Common difference is -4)==> nth term will be of A*n^2+B*n+C type.If in any other series, differences will be in A.P., then nth term =A*n+BIf differences of differences of differences are in A.P.,then nth term = A*n^3+B*n^2+C*n+DAnd so on
I had forgotten this 😛 Did a long time back.. Thanks for reminding though 
@anytomdickandhary said:48,100, 180, 294, 4481st difference: 52, 80, 114, 1542nd difference: 28, 34, 40 3rd difference: 6,6we see that third difference is constant hence general term must be a cubic using successive difference (not solving any eqn here!) we can find the coefficients ton^3+8n^2 + 21n + 18=(n+2)(n+3)^2hence sum upto 20 terms = 71830 Hence none of these.ATDH.
using successive difference (not solving any eqn here)
how sir, please elucidate
how sir, please elucidate
@vijay_chandola @anytomdickandhary sir.. your general terms are not matching in order of "x" Why so?? 
I couldn't understand..
I couldn't understand..
@anytomdickandhary said:48,100, 180, 294, 4481st difference: 52, 80, 114, 1542nd difference: 28, 34, 40 3rd difference: 6,6we see that third difference is constant hence general term must be a cubic using successive difference (not solving any eqn here!) we can find the coefficients ton^3+8n^2 + 21n + 18=(n+2)(n+3)^2hence sum upto 20 terms = 71830 Hence none of these.ATDH.
sir how did u found out this eqn n^3+8n^2 + 21n + 18??
@Brooklyn @bullseyes @ScareCrow28
bhaiyon dekho..
apna case hain c-b+a=0..... (1)
that gives us
(x+1)(ax+c).... (2)
also from eqn 1 and 2:
(x+1)(ax+(b-a))
now
value of a ::::::no ofvalues c can take
1 ::::::::::::::::::::::::2006 cases
2 ::::::::::::::::::::::::2005 cases
3 ::::::::::::::::::::::::2004 cases
..
..
so on..till
2007 :::::::::::::::::::::::1 case
hence total cases: (2006*2007)/2=1003*2007
kaha galat hain apna approach ?? 
@ScareCrow28 said:@vijay_chandola@anytomdickandhary sir.. your general terms are not matching in order of "x" Why so?? I couldn't understand..
Hey can you please elaborate on your question?
you can check that (n+2)*(n+3)^2 gives the terms of the sequence given for n=1,2,3....
Not very sure if I understand your question here.
ATDH.
@anytomdickandhary said:Hey can you please elaborate on your question?you can check that (n+2)*(n+3)^2 gives the terms of the sequence given for n=1,2,3....Not very sure if I understand your question here.ATDH.
sir, how did u get the coeff. without solving the equations ?
@anytomdickandhary said:Hey can you please elaborate on your question?you can check that (n+2)*(n+3)^2 gives the terms of the sequence given for n=1,2,3....Not very sure if I understand your question here.ATDH.
Sir, @vijay_chandola post above yours said that general term is a quadratic equation..while your solution says it to be a cubic equation. But your answers are same. I couldn't understand this anamoly(if here is any)