Question

Question # 16
The maximum sum of the A.P. 87, 83, 79,
is equal to:​

Answer 1

Answer:

hope you understand well mark it brilliant if you understand

Answer 2

Answer:

The maximum sum of the given AP is found to be 990.

Step-by-step explanation:

The given arithmetic progression sequence is having a negative common difference, so the maximum sum will come when no term is negative.

If the AP had started with the term 88 with the same common difference, the AP would include 0. So, the last positive term in the given AP will be 3 as there is a common difference of -4 and the first term is 87.

So, applying the expression of nth term of an AP: $a_n=a+(n-1)d$ and substituting the known information, we get:

$3=87+(n-1)(-4)$

Simplifying it, we get:

$4n-4=87-3$

$4n=84+4$

$4n=88$

or we can say:

$n=22$

Now, we have to find the sum of 22 terms of the given AP, so applying the expression of the sum of n terms of an AP: $S_n=\frac{n}{2}(a_n+a)$ and substituting the known information, we get:

$S_n=\frac{22}{2}(3+87)$

Simplifying it, we get:

$S_n=11(90)$

$S_n=990$

So, the maximum sum of the given AP is found to be 990.