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Brums [2.3K]
3 years ago
14

Write an explicit formula for the sequence and find the 18th term. -4, 12, -36...

Mathematics
2 answers:
lora16 [44]3 years ago
5 0

Answer:

Nth term = (4/3) × (-3)^n

18th term: 516560652 or 4 × 3¹⁷

Step-by-step explanation:

-4, 12 , -36...

Are terms of a Geometric progression with:

First term = -4

Common ratio = 12/-4 = -3

Nth term = -4 × (-3)^(n-1)

= -4 × (-3)^(n)/(-3)

= (-4/-3) ×3^n

= (4/3) × (-3)^n

18th term: n = 18

-4 × (-3)^(18-1)

-4 × (-3)¹⁷

4 × 3¹⁷

516560652

Molodets [167]3 years ago
4 0

Answer:

an = -4 * (-3)^ (n-1)

513560652

Step-by-step explanation:

We can find the common ratio

12/-4 = -3

r =-3

The explicit formula is

an =a1 r^(n-1)

an = -4 * (-3)^ (n-1)

We want the 18 th term

a 18 = -4 (-3) ^ 17

        513560652

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zavuch27 [327]

s = ut +  \frac{1}{2} a {t}^{2}  \\ s = 10( \frac{1}{2} ) +  \frac{1}{2} ( - 2) {( \frac{1}{2}) }^{2}  \\ s = 10( \frac{1}{2} ) +  \frac{1}{2} ( - 2)(  \frac{1}{4} ) \\ s = 5 + ( - 1)( \frac{1}{4} ) \\ s = 5 + ( -  \frac{1}{4} ) \\ s = 5 -  \frac{1}{4}  \\ s =  \frac{20}{4}  -  \frac{1}{4}  \\ s =  \frac{19}{4}

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Read 2 more answers
(1 point) consider the function f(t)=⎧⎩⎨⎪⎪⎪⎪0,−5,−6,6,t<00≤t<11≤t<7t≥7;f(t)={0,t<0−5,0≤t<1−6,1≤t<76,t≥7; 1. wr
sergij07 [2.7K]
f(t)=\begin{cases}0&\text{for }t

Recall that

u(t)=\begin{cases}0&\text{for }t

Take it one piece at a time. For t\ge0, we can scale u(t) by -5:

-5u(t)=\begin{cases}0&\text{for }t

If we shift the argument by 1 and scale by -5, we have

-5u(t-1)=\begin{cases}0&\text{for }t

so if we subtract this from -5u(t), we'll end up with

-5u(t)+5u(t-1)=\begin{cases}0&\text{for }t

For the next piece, we can add another scaled and shifted step like

-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t

so that

-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t

For the last piece, we add one more term:

6u(t-7)=\begin{cases}0&\text{for }t

and so putting everything together, we get f(t):

f(t)\equiv-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)+6u(t-7)
f(t)\equiv-5u(t)-u(t-1)+12u(t-7)
5 0
3 years ago
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