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
Masja [62]
2 years ago
12

How to use two terms to find a1,d, and an For the arithmetic sequence?

Mathematics
1 answer:
emmasim [6.3K]2 years ago
3 0

Answer:

  d = (a[n2] -a[n1])/(n2 -n1)

  a1 = a[n1] -d(n1 -1)

Step-by-step explanation:

The generic term is ...

  an = a1 +d(n -1)

Fill in the values associated with the two terms and solve the simultaneous equations.

For terms n1 and n2, their difference will be ...

  a[n2] -a[n1] = (a1 +d(n2 -1)) -(a1 +d(n1 -1)) = d(n2 -n1)

Dividing by the coefficient of d tells you ...

  d = (a[n2] -a[n1])/(n2 -n1)

Once you have the value of d, you can find the first term.

  a[n1] = a1 +d(n1 -1)

  a1 = a[n1] -d(n1 -1)

_____

<u>Example</u>:

  3rd term = 12

  7th term = 20

  d = (20 -12)/(7 -3) = 8/4 = 2

 a1 = a3 -d(3 -1) = 12 -2(2) = 8

The n-th term is ...

  an = a1 +d(n -1)

  an = 8 +2(n -1)

You might be interested in
Sean and sarah spend $70 a month eating out how much money would they have after 15 years if they invested the money instead at
SpyIntel [72]

Answer:

Future Value= $17,170.12

Step-by-step explanation:

Giving the following information:

Monthly deposit (A)= $70

Interest rate (i)= 0.04/12= 0.0033

Number of periods (n)= 15*12= 180 months

<u>To calculate the future value (amount saved), we need to use the following formula:</u>

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {70*[(1.0033^180) - 1]} / 0.0033

FV= $17,170.12

5 0
3 years ago
Kevin will take 4 math tests this term. All of the tests are worth the same number of points. After taking the first 3 tests, hi
Makovka662 [10]

Answer:

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

Step-by-step explanation:

we know that

The mean score is the total of all scores divided by the total number of tests.

Let

x_1 ----> the score in the first math test

x_2 ----> the score in the second math test

x_3 ----> the score in the third math test

x_4 ----> the score in the fourth math test

we have

After taking the first 3 tests, his mean test score is 88 points

so

\frac{x_1+x_2+x_3}{3} =88

x_1+x_2+x_3=264 ----> equation A

How many points does he need on his last test to raise his mean test score to 90 points?

so

\frac{x_1+x_2+x_3+x_4}{4} =90

x_1+x_2+x_3+x_4=360 ----> equation B

substitute equation A in equation B

264 + x_4 = 360

solve for x_4

x_4 = 360-264

x_4 = 96

Therefore

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

4 0
3 years ago
What is the simplified form of (x+3/x^2-x-12)•(x-4/x^2-8x+16)
iragen [17]
1/(x+4)2, hope this helped!
7 0
3 years ago
Someone please help... (needs work)
Gala2k [10]

..

............................

3 0
2 years ago
Consider the triangle reduction.
agasfer [191]

Answer:

10.8 Cm

.

.

.

ur welcome ♥️♥️♥️

3 0
3 years ago
Other questions:
  • PLEASE HELP ME 50 POINTS! AND BRAINLIEST IF YOU ARE CORRECT!
    15·1 answer
  • What is the constant proportionally of y=2.5x
    11·2 answers
  • A streetlight that is 9 feet tall casts a 2-foot-long shadow. A nearby flagpole casts a 11-foot-long shadow. What is the height
    8·1 answer
  • Is it easier to subtract when the numbers are written above each other?
    9·2 answers
  • How to factorise 7x+14
    14·1 answer
  • Two variables are correlated with r=−0.925. Which description best describes the strength and direction of the association betwe
    12·2 answers
  • Simplify the variable expression by evaluating its numerical part, and enter
    5·1 answer
  • What are equivalent expressions for <br> 3 (y + 1) + 4 + 3y
    7·1 answer
  • I need help with 1 through 10
    14·1 answer
  • Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!