Find the sum of the geometric series with a1 = 243, r = -2/3, and n = 5

Sum of 5 terms of give geometric series is 165.

Solution:

Need to find the sum of geometric series.  

Given that  

First term of geometric series = 243

Common ratio of geometric series r =

Number of terms in series = n = 5

Sum of geometric series when r < 1 is given by following formula

= 55 x 3 = 165  

Hence sum of 5 terms of give geometric series is 165.

john earns $14.00 for two hours of work.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form