# Math Help - Aritmetic progression in algebra

1. ## 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.

2. 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

3. Actually. This question was given in a book. I copied it as it is. The correct answer is 650.

4. Originally Posted by jashansinghal
Actually. This question was given in a book. I copied it as it is. The correct answer is 650.
Yes, you will get that answer if you follow my steps. Have you tried?