How many terms of the arithmetic sequence {-4,-2, 0, } will give a sum of 500? a. 25
b. 20
c. 50
d. 10

a. 25

Step-by-step explanation:

Sₙ = n/2 * (2 * a₁ + (n-1) * d)

Sₙ = 500     a₁ = -4    d = 2

500 = n/2 * (-8 + (n-1) * 2) = n/2 * (-8 + 2n - 2) = n/2 * (2n - 10) = n² -5n

n² - 5n -500 = 0

(n - 25) (n + 20) = 0

n > 0

n = 25

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1