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2 years ago

Find the first, fourth, and eighth terms of the sequence. A(n) = –3 • 2^n–1

1 answer:

4 0

A(n) = –3 • 2⁽ⁿ⁻¹⁾

for n = 1 , A₁ = -3.(2)⁰ = -3
for n = 2 , A₂ = -3.(2)¹ = -6
for n = 3 , A₃ = -3.(2)² = -12
for n = 4 , A₄ = -3.(2)³ = -24
...........................................
for n = 8 , A₈ = -3.(2)⁷ = -384

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WILL GIVE 100 POINTS

padilas [110]

(a) The explicit rule to model the sequence formed by the number of seats in each row is $a_{n}=15+3n$

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

$a_{n}=a+(n-1)d$ , where

a is the the first term
d is the common difference between each two consecutive terms

∵ There are 18 seats in the 1st row

∵ There are 21 seats in the 2nd row

∵ 21 - 18 = 3

∵ The number of seats is increased by 3 with each additional row

- The number of seats in each row represents an arithmetic

sequence because there is a common difference between

each two consecutive rows

∴ The number of seats in each row formed an arithmetic sequence

∵ The number of seats in the first row = 18 seats

∴ a = 18

∵ The number of seats in a row continues to increase by 3 with each

additional row

∴ d = 3

- Substitute the values of a and d in the rule of nth term

∴ $a_{n}=18+(n-1)3$

- Simplify the right hand side

∴ $a_{n}=18+3n-3$

- Add like terms

∴ $a_{n}=15+3n$

(a) The explicit rule to model the sequence formed by the number of seats in each row is $a_{n}=15+3n$

∵ There are 120 seat in a row

- Substitute $a_{n}$ by 120 in the rule above

∴ 120 = 15 + 3n

- Subtract 15 from both sides

∴ 105 = 3n

- Divide both sides by 3

∴ n = 35

∴ The number of the row is 35

(b) The 35th row has 120 seats

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

6 0

2 years ago

Select all that apply there are 3 red marbles, 5 green marbles, and 2 blue marbles in a bag. which of the following are true?

Zielflug [23.3K]

Answer:

3 red marbles

Step-by-step explanation:

4 0

2 years ago

I need help finding these three angles

Vsevolod [243]

Step-by-step explanation:

[ Refer to the attachment ]

8 0

2 years ago

URGENT HELP ME PLEASE

Trava [24]

Answer:

(a) $\log_3(\dfrac{81}{3})=3$

(b) $\log_5(\dfrac{625}{25})=2$

(d) $\log_4(\dfrac{64}{16})=1$

(e) $\log_6(36^4)=8$

(f) $\log(100^3)=6$

Step-by-step explanation:

Let as consider the given equations are $\log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?$ .

(a)

$\log_3(\dfrac{81}{3})=\log_3(27)$

$\log_3(\dfrac{81}{3})=\log_3(3^3)$

$\log_3(\dfrac{81}{3})=3$ $[\because \log_aa^x=x]$

(b)

$\log_5(\dfrac{625}{25})=\log_5(25)$

$\log_5(\dfrac{625}{25})=\log_5(5^2)$

$\log_5(\dfrac{625}{25})=2$ $[\because \log_aa^x=x]$

(c)

$\log_2(\dfrac{64}{8})=\log_2(8)$

$\log_2(\dfrac{64}{8})=\log_2(2^3)$

$\log_2(\dfrac{64}{8})=3$ $[\because \log_aa^x=x]$

(d)

$\log_4(\dfrac{64}{16})=\log_4(4)$

$\log_4(\dfrac{64}{16})=1$ $[\because \log_aa^x=x]$

(e)

$\log_6(36^4)=\log_6((6^2)^4)$

$\log_6(36^4)=\log_6(6^8)$

$\log_6(36^4)=8$ $[\because \log_aa^x=x]$

(f)

$\log(100^3)=\log((10^2)^3)$

$\log(100^3)=\log(10^6)$

$\log(100^3)=6$ $[\because \log10^x=x]$

5 0

3 years ago

When you graph an inequality, you used a closed dot when you use which<br> symbols?

aksik [14]

You use a closed dot with the greater than or less than with the line under the symbol or the greater than or equal to or the less than or equal to symbols. The line indicates a closed dot.

8 0

2 years ago