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

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.