Mathematics, 21.03.2020 11:22 aero8030

What is the sum of the first five terms of a geometric series with a1=6 and r= 1/3

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Answer from: glamourgirlno1foev

the sum of the first 5 terms is 8.96

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = a(1 - r^n)/(1 - r)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = 6

r = 1/3

n = 5

Therefore, the sum of the first 5 terms, S5 is

S5 = 6(1 - 1/3^5)/(1 - 1/3)

S5 = 6(1 - 1/243)/(2/3)

S5 = 6(242/243)/(2/3)

S5 = (1452/243)/(2/3)

S5 = (1452/243) × (3/2)

S5 = 4356/486

S5 = 8.96

Answer from: Quest

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative. remember to flip the inequality when taking the negative solution

x-4 < 1 x-4 > -1

add 4 to each side

x-4+4 < 1+4 x-4+4 > -1+4

x< 5 x> 3

3< x< 5

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is