Question

What is the summation notation for the series? 200+175+150+125+___+(-300)

Answer 1

21
E (225-25n)
n=1
So its D.

Answer 2

Sum notation will be
`\sum_(n=1)^(21)(225-25n)`

Explanation:

The given series is 200 + 175 + 150 + 125........+(-300)

Here
`T_(n)=a+(n-1)d`

a = 200

d = -25

T(n) = -300

Therefore from the equation

-300 = 200 + (n-1)(-25)

200 -25n + 25 = -300

225 - 25n = -300

-25n = -300 - 225 = -525

n = (-525)/(-25) = 21

Now
`T_(n)=200+(n-1)(-25)`

`T_(n)= 200+25-25n = (225-25n)`

Now the notation will be

`\sum_(n=1)^(21)(225-25n)`