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4 years ago

6

Write a formula for the general term or nth term for the sequence. Then find the indicated term. five halves comma five fourths

comma five eighths comma five sixteenths ...; a 8 a Subscript nequals ?

1 answer:

nadya68 [22]4 years ago

6 0

Sequence: 5/2, 5/4, 5/8, 5/16
a8=?

a1=5/2
a2=5/4
a3=5/8
a4=5/16

a2/a1=(5/4)/(5/2)=(5/4)*(2/5)=(5*2)/(4*5)=2/4=1/2
a3/a2=(5/8)/(5/4)=(5/8)*(4/5)=(5*4)/(8*5)=4/8=1/2
a4/a3=(5/16)/(5/8)=(5/16)*(8/5)=(5*8)/(16*5)=8/16=1/2
Ratio: r=a2/a1=a3/a2=a4/a3→r=1/2

an=a1*r^(n-1)
a1=5/2, r=1/2
an=(5/2)*(1/2)^(n-1)
an=(5/2)*[1^(n-1)/2^(n-1)]
an=(5/2)*[1/2^(n-1)]
an=(5*1)/[2*2^(n-1)]
an=5/2^(1+n-1)
an=5/2^n

n=8→a8=5/2^8
a8=5/256

Answers:
The formula for the general term or nth term for the sequence is an=5/2^n
a8=5/256

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Answer:

$16,000 at 8% annual interest.

$12,000 at 6% annual interest.

Step-by-step explanation:

Let x be amount invested at a rate of 8% annual interest and y be the amount invested at a rate of 6% annual interest.

We have been given that an executive invests $28000, some at 8% and the rest at 6% annual interest. We can represent this information as:

$x+y=28,000...(1)$

We are also given that he received annual return of $2000. We can represent this information as:

$(\frac{8}{100})x+(\frac{6}{100})y=2,000...(2)$

$0.08x+0.06y=2,000...(2)$

We will use substitution method to solve our system of equations. From equation (1) we will get,

$x=28,000-y$

Substituting this value in equation (2) we will get,

$0.08(28,000-y)+0.06y=2,000$

$2240-0.08y+0.06y=2,000$

$2240-2240-0.08y+0.06y=2,000-2240$

$-0.08y+0.06y=2,000-2240$

$-0.02y=-240$

$\frac{-0.02y}{-0.02}=\frac{-240}{-0.02}$

$y=12,000$

Therefore, the executive has invested $12,000 at a rate of 6% annual interest.

Upon substituting y=12,000 in equation (1) we will get,

$x+12,000=28,000$

$x+12,000-12,000=28,000-12,000$

$x=16,000$

Therefore, the executive has invested $16,000 at a rate of 8% annual interest.

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Let x be the selling price of the bicycle.

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