Respuesta :

fieryanswererft

PART (A):

As the total amount increases double each month. It is a geometric sequence equation. Fill the table.

Geometric Sequence: y = a(r)ˣ⁻¹

Here given:
First term (a) = 40
Common Difference (d) = 2

Equation: y = 40(2)ˣ⁻¹

After 1 year: y = 40(2)¹²⁻¹ = $81920

[tex]\rule{300}{1}[/tex]

PART (B):

As the amount increases by $50 each month. It is a arithmetic or linear sequence.

Linear Equation: y = mx + b

Here given:
slope (m) = 50
starting (b) = 30

Equation: y = 50x + 30

After 1 year: y =  50(12) + 30 = 630

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#a

Use geometric progression formula

  • y=ar^{n-1}

Here

  • r=2

First term =2(20)=40

  • a=40

Equation

[tex]\\ \rm\Rrightarrow y=40(2)^{n-1}[/tex]

After a year

[tex]\\ \rm\Rrightarrow y=40(2)^{11}[/tex]

[tex]\\ \rm\Rrightarrow y=40(2048)[/tex]

[tex]\\ \rm\Rrightarrow y=\$81920[/tex]

#b

It's arithmetic as common difference is 50

[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]

Equation

  • First term =30+50=80

[tex]\\ \rm\Rrightarrow a_n=80+(n-1)50[/tex]

After a year

[tex]\\ \rm\Rrightarrow a_{12}=80+11(50)[/tex]

[tex]\\ \rm\Rrightarrow 80+550[/tex]

[tex]\\ \rm\Rrightarrow \$630[/tex]

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