1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inysia [295]
3 years ago
15

Identify the 42nd term of an arithmetic sequence where a_1=-12 and a_27=66

Mathematics
2 answers:
baherus [9]3 years ago
7 0

Answer:

111

Step-by-step explanation:

Arithmetic sequences are linear. That means no matter the pair of points use to calculate slope, or common difference, that number remains constant.

We are given points (1,-12) and (27,66) are on the line.

Calculating slope by subtracting points and then putting 2nd number over 1st.

(27,66)

(1, -12)

-----------subtracting

26 , 78

The slooe or the common difference is 78/26=3.

So now we want to know n such that (42,n) is on this same line.

Let's use the slope formula again with (42,n) and (1,-12).

(42,n)

( 1,-12)

----------subtracting

41 , n+12

The slope is (n+12)/41 but we have also calculated it to be 3 so these expressions are equal.

(n+12)/41=3

Multiply both sides by 41:

n+12=123

Subtract 12 on both sides.

n=111

Wittaler [7]3 years ago
3 0

Answer:

a₄₂ = 107

Step-by-step explanation:

The nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂₇ = 66 , then

a₁ + 26d = 66 , that is

- 12 + 26d = 66 ( add 12 to both sides )

26d = 78 ( divide both sides by 26 )

d = 3

Then

a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111

You might be interested in
What is the inverse of the function f(x) = 2x + 1?
BaLLatris [955]

Answer:

f^{-1} = \frac{x-1}{2}

Step-by-step explanation:

f(x) = 2x+1

<em>Replace it with y</em>

y = 2x+1

<em>Exchange the values of  x and y</em>

x = 2y+1

<em>Solve for y</em>

x = 2y+1

<em>Subtracting 1 from both sides</em>

2y = x-1

<em>Dividing both sides by 2</em>

y = \frac{x-1}{2}

<em>Replace it by </em>f^{-1}

So,

f^{-1} = \frac{x-1}{2}

3 0
3 years ago
Read 2 more answers
Charlie saves $21.45 each month for 6 months.In the seventh month, he only saves $10.60.How much money will Charlie have after 7
Tomtit [17]
$21.45 x 6 = $128.7
$128.7 + $10.60 = $139.3

Charlie will have saved $139.3 in 7 months
8 0
3 years ago
HELP ME PLEASE WITH THIS QUESTION!!!!!!!!!!!
allochka39001 [22]
I think you have to divide
7 0
3 years ago
Help me with this problem show your work please
Akimi4 [234]
It cannot be simplified...
5 0
3 years ago
The next number in the arithmetic sequence 10,23,36,? Is
rjkz [21]
It would be 49
10+13=23
23+13=36
36+13=49
I think this is right
6 0
3 years ago
Other questions:
  • What is the domain of the function y=^3√x+8
    11·1 answer
  • Which equation represents the slope-intercept form of the line below? y intercept: 0, 8 slope : 1/2
    5·1 answer
  • A family consists of a father, a mother and 2 children. What is the probability that all 2 children are boys?
    7·1 answer
  • NEED MAJOR HELP ASAP!!!!!
    15·1 answer
  • The coordinate of M is 3.5 and MN
    15·1 answer
  • What is the point of intersection when y=4-x 2y=8-2x
    13·1 answer
  • What is the y-intercept of the linear equation y=5x+7
    10·2 answers
  • Find the slope for me no?ill give more point for right answer​
    9·1 answer
  • Dinner for a family of 3 at the local Italian Eatery came to $47.83 before tax. If the family wanted to tip their server 20%, ho
    9·1 answer
  • Determine the radius and center of the circle with the following equation <br> x^2+y^2-12x+24y-10=6
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!