Latest TCS Aptitude Question SOLUTION: assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1).for all natural no(integer>0)m and n.what is the value of f(17)?

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assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1).for all natural no(integer>0)m and n.what is the value of f(17)?

Asked In TCS litun (10 years ago)

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surbhi rathaur  (10 years ago)

4832...
calculate upto f(5)by putting values in the given expression i.e. f(1)=0, f(2)=32, f(3)=100, f(4)=204, f(5)=344. then cal f(7)=f(5+2)orf(3+4)=732 and f(10)=f(5+5)=1584, and now f(17)=f(10+7)=f(10)+f(7)+4(9*15*7 -1)..........
f(17)=1584+732+2516=4832

Is this solution Helpfull? Yes (70) | No (5)  

Manish Kumar  (10 years ago)

f(2) = f(1+1)=f(1)+f(1)+4(9*1*1 - 1 )= 0+0+4*8 = 32
f(4) = f(2+2)=f(2)+f(2)+4(9*2*2 - 1 )= 32+32+4*35 = 204
f(8) = f(4+4)=f(4)+f(4)+4(9*4*4 - 1 )= 204+204+4*143 = 980
f(16) = f(8+8)=f(8)+f(8)+4(9*8*8 - 1 )= 980+980+4*575 = 4260
f(17)= f(1+16)= f(16)+f(1)+4(9*16*1 -1)= 4260+0+ 4*143= 4832

Is this solution Helpfull? Yes (64) | No (2)  

Rishabh Purwar  (10 years ago)

f(2) = f(1+1)=f(1)+f(1)+4(9*1*1 - 1 )= 0+0+4*8 = 32
f(4) = f(2+2)=f(2)+f(2)+4(9*2*2 - 1 )= 32+32+4*35 = 204
f(8) = f(4+4)=f(4)+f(4)+4(9*4*4 - 1 )= 204+204+4*143 = 980
f(16) = f(8+8)=f(8)+f(8)+4(9*8*8 - 1 )= 980+980+4*255 = 2980
f(17)= f(1+16)= f(1)+f(16)+4(9*16*1 -1)= 0+ 2980 + 4*143= 3552

Is this solution Helpfull? Yes (13) | No (12)  

Anuja Singh  (10 years ago)

4(9-1)+4(9*2-1)+4(9*3-1)+........+4(9*16-1)
4[9(1+2+3+.....+16)-16]
4[9*16*17/2-16]
4832

Is this solution Helpfull? Yes (6) | No   

Bhavesh Srivastava  (10 years ago)

f(16+1)=f(16)+f(1)+4((9*16*1)-1)=f(16)+0+(4*143)
f(16)=f(15+1)=f(15)+0+(4*((9*16*1)-1)
.....
f(2)=f(1+1)=f(1)+f(1)+(4((1*1*9)-1)
therefore series formed will be
f(17)=4*((9*1)+(9*2)+(9*3)..........(9*16))
f(17)=4832

Is this solution Helpfull? Yes (3) | No (1)  

SumithraRengaraj  (9 years ago)

f(2) = f(1+1)=f(1)+f(1)+4(9*1*1 - 1 )= 0+0+4*8 = 32
f(4) = f(2+2)=f(2)+f(2)+4(9*2*2 - 1 )= 32+32+4*35 = 204
f(8) = f(4+4)=f(4)+f(4)+4(9*4*4 - 1 )= 204+204+4*143 = 980
f(16) = f(8+8)=f(8)+f(8)+4(9*8*8 - 1 )= 980+980+4*575 = 4260
f(17)= f(1+16)= f(16)+f(1)+4(9*16*1 -1)= 4260+0+ 4*143= 4832

Is this solution Helpfull? Yes (3) | No   

shikha verma  (10 years ago)

1047..by f(9+8)

Is this solution Helpfull? Yes (1) | No (3)  

Guru Pranav  (10 years ago)

f(1)=0, f(2)=32, f(3)=100, f(4)=204, f(5)=344.

f(17)=1584+732+2516=4832. Ans

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Manish Kumar  (10 years ago)

Unit digit is 6.

Is this solution Helpfull? Yes | No (4)  

utkarsh bisht  (10 years ago)

ans will be 5032

Is this solution Helpfull? Yes | No (11)  

Avinash Kumar  (10 years ago)

answer is 6

Is this solution Helpfull? Yes | No (9)  

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