Aritmetic progression in algebra

• Jun 20th 2010, 02:04 AM
jashansinghal
Aritmetic progression in algebra
f(x)+ 2x, where x is an integer. If we arrange the values f(x) for x= 25,24,23,.....(continuously decreasing value of x), we get an arithmetic progression whose first term is 50. Find the maximum value of the sum of all the terms of A.P.
• Jun 20th 2010, 03:56 AM
Quote:

Originally Posted by jashansinghal
f(x)+ 2x, where x is an integer. If we arrange the values f(x) for x= 25,24,23,.....(continuously decreasing value of x), we get an arithmetic progression whose first term is 50. Find the maximum value of the sum of all the terms of A.P.

i think you mean f(x)=2x

Identify all values of x which makes f(x) positive , ie 25 ,... ,1 since f(0)=0 and f(-1)=-2 ,f(x) will be -ve since then.

f(25)=50 , f(1)=2

This AP has first term 50 and last term 2 with common difference -2 ,evaluate the sum then
• Jun 20th 2010, 04:00 AM
jashansinghal
Actually. This question was given in a book. I copied it as it is. The correct answer is 650.
• Jun 20th 2010, 04:05 AM