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
Anna007 [38]
2 years ago
9

An arithmetic sequence has t1=5 and t2=8 find tn and sn

Mathematics
1 answer:
RoseWind [281]2 years ago
4 0

Answer:

a_n=2+3n

\displaystyle S_n=\frac{7n+3n^2}{2}

Step-by-step explanation:

<u>Arithmetic Sequences </u>

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

a_n=a_1+(n-1)r

Where

an = nth term

a1 = first term

r   = common difference

n  = number of the term

The sum of the n terms of an arithmetic sequence is given by:

\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n

We are given the first two terms of the sequence:

a1=5, a2=8. The common difference is:

r = 8 - 5 = 3

Thus the general term of the sequence is:

a_n=5+(n-1)3=5+3n-3=2+3n

\boxed{a_n=2+3n}

The formula for the sum is:

\displaystyle S_n=\frac{5+2+3n}{2}\cdot n

\displaystyle S_n=\frac{7+3n}{2}\cdot n

Operating:

\boxed{\displaystyle S_n=\frac{7n+3n^2}{2}}

You might be interested in
Christian reads 1/4 of a book every 2/3 weeks how many books does Christain read per week​
vredina [299]

Answer:

3/8 of a book per week

Step-by-step explanation:

6 0
2 years ago
Over the course of 2 hours, Abe assembled 18 plastic toys. If Abe continues assembling toys at this rate, which proportion can b
Kaylis [27]

Answer: 126

Step-by-step explanation: multiply 7 times 18 toys 7 for the hours and 18 fr the toys and you will get 126

3 0
2 years ago
jeanine Baker makes floral arrangements. She has 13 different cut flowers and plans to use 7 of them. How many different selecti
Ksju [112]

A total of 1,716 selections of the 7 flowers are possible.

Step-by-step explanation:

Step 1:

There are 13 flowers from which Jeanine Baker plans to use 7 of them.

To determine the number of selections that are possible we use combinations.

The formula for combinations is; ^{n} C_{r}=\frac{n !}{(n-r) ! r !}.

Step 2:

In the given formula, n is the total number of options and r is the number of options to be selected.

For this question, n = 13 and r=7.

So ^{13} C_{7}=\frac{13 !}{(13-7) ! 7 !} = \frac{13 !}{(6) ! 7 !} = 1,716.

So a total of 1,716 selections are possible.

3 0
3 years ago
Belle walks 7/10 mile each morning, and 1, 4/10 miles each evening.
kow [346]

Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

7 0
2 years ago
Read 2 more answers
Help please I’m on a timer
iren2701 [21]
All real numbers greater than or equal to -3
7 0
3 years ago
Other questions:
  • What is 789,626,968,486,998 -1
    14·2 answers
  • Find the greatest common factor of 11x2 and 7c .
    10·1 answer
  • Charlotte has been working for her company for x years. Travis has been working for the same company exactly 3 years longer than
    8·2 answers
  • Square root of 50 estimated to the nearest integer
    8·2 answers
  • Solve for x in the diagram below.<br> (2 +40)<br> 60°
    12·2 answers
  • Which coordinate does the axis of symmetry represent?
    14·1 answer
  • When invested at an annual interest rate of 4.7%, an account earned $1,290.33 of simple
    8·2 answers
  • WHO HAS THIS PAGE ????????
    9·1 answer
  • Use the information to find the percent change.
    8·2 answers
  • find three consecutive integers for which 3 times the sum of the first and third integers is -342? show step by step
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!