Answer:
The sum of the arithmetic progression is 2520
Step-by-step explanation:
The sum, Sₙ, of an arithmetic progression, AP, is given as follows;
[tex]S_{n}=\dfrac{n}{2}\cdot \left (2\cdot a+\left (n-1 \right )\cdot d \right )[/tex]
Where;
n = The nth term of the progression
a = The first term = 100
d = The common difference = -2
Given that the last term = -10, we have;
-10 = 100 + (n - 1) ×(-2)
n = (-10 - 100)/(-2) + 1 = 56
Therefore, the sum of the 56 terms of the arithmetic progression is [tex]S_{56}=\dfrac{56}{2}\cdot \left (2\cdot 100+\left (56-1 \right )\cdot (-2) \right )[/tex]
Which gives;
[tex]S_{56}={28}\cdot \left (200-\left 110 \right ) = 2520[/tex]
