All categories

3 years ago

Arithmetic Sequences Continued

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

5 0

Answer:

The common difference is 4

5, 9, 13, 17

Step-by-step explanation:

Given

5, _, _, 17

Solving (a): The common difference

Since it is an arithmetic sequence, the common difference can be solved using:

$T_n = a + (n - 1)d$

Where

$a = 5$

$T_n = 17$

$n = 4$ i.e. 4 terms

So:

$T_n = a + (n - 1)d$

$17 = 5 +(4 - 1) * d$

$17 = 5 +3d$

Collect like terms

$3d = 17 - 5$

$3d = 12$

$d =4$

Hence, the common difference is 4

Solving (b): Complete the blanks.

To do this, we simply add 4 to each successive terms.

So: 5, 9, 13, 17

You might be interested in

Need to know the area of the composite figure.

Deffense [45]

Answer:

51 m^2

Step-by-step explanation:

The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.

The applicable formulas are ...

area of a triangle:

A = (1/2)bh

area of a rectangle:

A = bh

area of a trapezoid:

A = (1/2)(b1 +b2)h

___

We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...

A = (1/2)(16 m + 10 m)(5 m) = 65 m^2

The area of the white internal rectangle is ...

A = (2 m)(7 m) = 14 m^2

So, the shaded area is the difference:

65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure

_____

Alternate approach

Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...

(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2

= 51 m^2

7 0

3 years ago

Please help me! what’s the answer? 1) Two points 2) One point 3) One equation

Fiesta28 [93]

Answer:

I think 2 points

Step-by-step explanation:

I may be wrong bc I suck at algebra. literally who is gonna use algebra ever?

4 0

3 years ago

Read 2 more answers

The price of a visit to the dentist is \$50$50. If the dentist fills any cavities, an additional charge of \$100$100 per cavity

kenny6666 [7]

Answer:300

Step-by-step explanation:

um i dk know if the two 50$ means any thing but thats what i got

7 0

3 years ago

Olivia has taken an initial dose of a prescription

mrs_skeptik [129]

Answer:

0.56 milligrams

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

M(6) = 50·e^(-0.75·6) = 50·e^-4.5 ≈ 0.56 . . . . milligrams

8 0

3 years ago

How would i anser this select all the ratios equivalent to 4:6

Natali5045456 [20]

If we try to simplify the ratio or try to multiply both by any number, we will get the equivalent ratio

Like :

$\frac{4}{6} \\$

Divide ( simplify ) by 2

$\frac{ \frac{4}{2} }{ \frac{6}{2} } \\ \\ \\ = > \frac{2}{3}$

Or multiply by any number,

$\frac{4}{6} \\ \\ \\ = > \frac{4 \times 2}{6 \times 2} \\ \\ \\ = > \frac{8}{12}$

From the example, 2 / 3 and 8 / 12 are equivalent ratios to 4 / 6

6 0

3 years ago