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3 years ago

Write the first 6 terms of the arithmetic sequence whose first term is 8 and has a common difference of 2

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

6 0

Answer: The first 6 terms are = 8, 10, 12,14,16,18

Step-by-step explanation:

The NTH term of an Arithmetic Sequence is given as

an = a1 + (n - 1 ) d

where a1 = First term given as 8 and

d= common difference given as 2

Therefore We have that

the first term

an = a1 + (n - 1 ) d = 8+(1-1) 2

a1= 8

second term=

an = a1 + (n - 1 ) d= a2= 8 + (2-1) 2

= 8+ 2(1) = 10

3rd term

an = a1 + (n - 1 ) d= a3= 8 + (3-1) 2

= 8+ 2(2)= 8 + 4=12

4th term

an = a1 + (n - 1 ) d= a4= 8 + (4-1) 2

= 8+ 2(3)= 8+6=14

5th term

an = a1 + (n - 1 ) d= a5= 8 + (5-1) 2

= 8+ 2(4)=8+ 8=16

6th term

an = a1 + (n - 1 ) d= a6= 8 + (6-1) 2

= 8+ 2(5)=8 +10 =18

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Arada [10]

Answer:

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Step-by-step explanation:

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First open the parentheses by applying the distributive property.

To do this, multiply each term you have inside (-3x⅔ + 5x + 7) by -1.

Thus, you would have the following:

12x² + 2x + 3x² - 5x - 7

Add like terms

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3 years ago

On Melissa's 6th birthday, she gets a $2000 CD that earns 7% interest compounded quarterly. If the CD matures on her 13th birthd

Alexandra [31]

Answer:

$A\simeq3250.83$

Step-by-step explanation:

The amount formula in compound interest is:

$A=P(1+\frac{r}{n} )^{nt}$

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $2000

$r = 7\% = \frac{7\%}{100\%}=0.07$

t = 7 (number of years from 6th to 13th bday)

n = 4 (quarterly in a year)

Then,

$A=2000(1+\frac{0.07}{4} )^{(4)(7)}\\\\A=2000(1+\frac{0.07}{4} )^{28}\\\\A=3250.825792\\\\A\simeq3250.83$

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3 years ago

Does anyone know how to solve this??

sergij07 [2.7K]

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3 years ago

1. Bob is looking to buy a new baseball cap with his favorite team’s logo on it. He finds one that normally sells for $32. If a

GenaCL600 [577]

Answer:

The total cost is $34.24.

Step-by-step explanation:

Given : Bob is looking to buy a new baseball cap with his favorite team’s logo on it. He finds one that normally sells for $32. If a 7% sales tax is added.

To find : What is the total cost?

Solution :

The sales price = $32

The tax rate = 7%=0.07

The sales tax is given by,

$\text{Sales tax}=\text{Rate}\times \text{Price}$

$\text{Sales tax}=0.07\times 32$

$\text{Sales tax}=2.24$

Now, adding to sales price

Total cost = 32+2.24

Total cost = $34.24

Therefore, the total cost is $34.24.

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3 years ago

A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is

Virty [35]

Answer:

See below

Step-by-step explanation:

The side of the square is w/2, then its area is:

A = (w/2)² = w²/4

The shaded area is the difference of areas of the rectangle and the square:

14w - w²/4 = 84

This can be simplified:

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8 0

3 years ago