Question

The maximum value of sum of the ap 50,48,46,44....

Answer 1

Hey mate
In order to find maximum value of sum we need to make sure that there us no negative term as it will reduce the value.
So, a= 50 and d= -2
nth term must be positive so
a + (n-1)d > 0
50 -2n +2 > 0
n < 26
n = 25 26th term is 0
Sum of first 25 terms = n [2a + (n-1)d]/2
= 25 [100 - 48] / 2
= 650 is the answer

Answer 2

Given:

50,48,46,44....

First-term a= 50

Common difference d= -2

To find:

The maximum value of the sum of the ap 50,48,46,44....

Solution:

In order to find the maximum value of the sum, no negative term should be there as it will reduce the value.  

a + (n-1)d > 0

50 -2n +2 > 0

n < 26

n = 25 (26th term is 0)

Sum of first 25 terms = n [2a + (n-1)d]/2

                                   = 25 [100 - 48] / 2

                                   = 650

Hence, the maximum value of the sum of the AP is 650.