All categories

3 years ago

In a certain arithmetic sequence, if -4 is the first term and 10 is the third term, which term is 157?

Mathematics

2 answers:

MAXImum [283]3 years ago

5 0

Answer:

157 is the 24th term

Step-by-step explanation:

The formula for arithmetic sequences is an=a1+(n-1)d,

where an is the nth term, a1 is the first term, n is the term position, and d is the common difference

First, we need to find the common difference using the 10.

Since it's the third term, we have 10=-4+(3-1)d

Solving for d gives us d=7

Next, we need to find the term number of 157

Thus, we have 157=-4+(n-1)*7

Solving for n gives us n=24

We can check it like this: Following order of operations (i.e. PEMDAS) gives us 24-1=23*7=161-4=157

likoan [24]3 years ago

4 0

Answer:

a₁₅₇ = 1,088

Step-by-step explanation:

aₙ = a₁ + d(n-1); where 'd' if common difference

a₁₅₇ = -4 + 7(156)

= -4 + 1092

= 1,088

You might be interested in

My number is the first multiple of 3,6, and 9 what is my number

Paladinen [302]

Answer:

18 is the first multiple of 3,6, and 9.

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

YOU KNOW THE DRILL 2.0

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.

6 0

3 years ago

A regular decagon has a radius of 14'. Determine the length of the apothem. Then determine the perimeter of the decagon

pav-90 [236]

Answer:

Part 1) The length of the apothem is 13.32'

Part 2) The perimeter of the decagon is 86.5'

Step-by-step explanation:

we know that

A regular decagon has 10 equal sides and 10 equal interior angles

A regular decagon can be divided into 10 congruent isosceles triangle

(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)

The vertex angle of each isosceles triangle is equal to

$\frac{360^o}{10}=36^o$

To find out the side length of the decagon, we can use the law of cosines

$c^2=a^2+b^2-2(a)(b)cos(C)$

where

c is the length side of decagon

a and b are the radii

we have

$a=14'\\b=14'\\C=36^o$

substitute the values

$c^2=14^2+14^2-2(14)(14)cos(36^o)$

$c^2=392-(392)cos(36^o)$

$c=8.65'$

To fin out the perimeter of decagon multiply the length side by 10

$P=8.65(10)=86.5'$

To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle

see the attached figure to better understand the problem

$r^2=a^2+(c/2)^2$

substitute the given values

$14^2=a^2+(8.65/2)^2$

solve for a

$a^2=14^2-(8.65/2)^2$

$a=13.32'$

8 0

3 years ago

the sides of a rectangle are in the ratio 5:7 and the perimeter of the rectangle is 96cm. What is the area of the rectangle?

dlinn [17]

Width = 5x
length = 7x

Perimeter = 10x + 14x = 24x = 96cm
x = 96/24 = 4cm

width = 5x = 20cm
length = 7x = 28cm

Area = (20cm x 28cm) = 560 cm²

6 0

3 years ago

Which will result in a difference of squares?

SIZIF [17.4K]

Answer:

The expression which will result in difference of two squares is:

(–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

(a-b)(a+b)=a²-b²

i.e. it is a difference of two square quantities. (a^2 and b^2)

since,

a= -7x , b=4

(-7x+4)(-7x-4)= (-7x)² - (4)²

=(7x)² - 4²

So the expression is a difference of two square quantities:

(7x)² and (4)²

Hence the answer is (–7x + 4)·(–7x – 4)....

5 0

3 years ago