Mathematics, 12.01.2021 05:40 brianrodriguez2005

Find the 14th term of the geometric sequence 6, -18,54, ...

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Answer from: hhvgbv7147

The 14th term of the geometric sequence 6, -18,54, ... is -9,565,938

Geometric series

Given:

6, -18, 54, ...

First term, a = 6

Common ratio, r = a2 ÷ a1

= -18 / 6

= -3

nth term of a geometric series = ar^n -1

14th term = 6 × -3^(14-1)

= 6 × -3^13

= 6 × -1,594,323

= -9,565,938

Therefore, 14th term of the geometric sequence 6, -18,54, ... is -9,565,938

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Answer from: eduardoma2902

Step-by-step explanation:

first term (t1) = 6 (a)

Second term (t2) = - 18

Common ratio (r) = t2/ t1 = - 18 / 6 = -3

Now

14th term (t14)

$a {r}^{14 - 1}$

$6 \times ( - 3)^{13}$

= 6 X - 1594323

= 9565938

Answer from: Quest

Best answer that i found on yahoo ok set : x= length of 2nd piece in cm x- 3= length of 1st piece in cm x-4= length of 3rd piece in cm then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20 3x - 7= 20 3x= 27 x= 9 the shortest piece is the third piece which is x- 4 x-4 9-4 = 5 the length of the smallest piece is 5 cm. the other lengths are 9 cm 6 cm

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

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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Find the 14th term of the geometric sequence 6, -18,54, ......

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