The sum of the first 6 terms of a geometric series is 15,624 and the common ratio is
5 find the first term of the series

4

Step-by-step explanation:

The sum of the first n terms of a geometric series is:

S = a₁ (1 − rⁿ) / (1 − r)

Given S = 15624, r = 5, and n = 6:

15624 = a₁ (1 − 5⁶) / (1 − 5)

a₁ = 4

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is