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
yarga [219]
3 years ago
10

The arithmetic series 15+18+21+...+84+87 has how many terms?

Mathematics
2 answers:
bearhunter [10]3 years ago
8 0

We can use the general term of the arithmetic series. Look:


\mathsf{a_n=a_1+(n-1)\cdot r}


Where:


\mathsf{a_1}: first term, 15.

\mathsf{a_n}: last term, 87.

n: number of terms (what we looking for);

r: reason, which is equal to the difference between two terms, that is, 3.


Let's go to the calculations.


\mathsf{a_n=a_1+(n-1)\cdot r}\\\\ \mathsf{87=15+(n-1)\cdot3}\\\\ \mathsf{87-15=(3n-3)}\\\\ \mathsf{72=3n-3}\\\\ \mathsf{72+3=3n}\\\\ \mathsf{75=3n}\\\\ \mathsf{n=\dfrac{75}{3}=25}


There are 25 terms.

Advocard [28]3 years ago
7 0

Answer:

The series has 25 terms.

Step-by-step explanation:

You could just diligently count, but it looks much better if you use the formula for the n-th term of an arithmetic series like this:

x_k = 15 + 3k\,\,,k=0,1,...

so the k=0 term is 15,  k=1 is 18, etc. Now we solve an equation as follows:

15+3k=87\implies k = (87-15)/3=24

so the last term (87) occurs for k=24, which means, including the 0-th term, there are 25 terms in this series.

The advantage of this method is that it would work for very very long series just as nicely, like 15+18+21+...+ 3015, 3018 (where the diligent method would just be way too boring)

You might be interested in
True or False: You can be considered a living thing even without a DNA based genetic code,
Illusion [34]

Answer:

True

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
An appliance company uses the function f(h) = 40h + 120 to calculate the total repair bill, f(h), for h number of hours worked.
Verdich [7]

Answer:

fh. = 40h + 120,  fh. = $200

200 = 40h + 120

200 - 120 = 40h

80 = 40h

80/40  = h

 2 = h

h = 2 hours.

Step-by-step explanation:

4 0
3 years ago
What is the value of 3 in the following numbers 6.13​
expeople1 [14]

Answer:

3 hundredths or .03

Step-by-step explanation:

3 0
3 years ago
Please help me and I’ll give you brainiest!!!!!!!!! <br><br> Thank you:)!!!!!
sattari [20]
What you have written down is correct, x=-3
4 0
3 years ago
Raj used 4 3/4 cups of sugar for each batch of muffins. He made 3 1/2 batches. Raj used 16 5/8 cups of sugar altogether.
saul85 [17]

Answer:

It is true!

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Q8 Q17.) Find the numbers.
    8·2 answers
  • Heather is going to graph y= -3x^2 +3. How is the parent graph transformed
    10·1 answer
  • Given that (-9,-1) is on the graph of f(x) find the corresponding point for the function f(x+3).
    8·1 answer
  • PLEASE HELPPPPPPLPPPPPPPP
    8·1 answer
  • The diaz family arrived for breakfast at a diner at 8:45 a.M .They stayed at the diner for 1 hour and 23 minutes. What time did
    10·1 answer
  • What is the value of this expression when g=-3.5?
    11·1 answer
  • The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer in simple
    10·2 answers
  • Solve for x.<br> Sqrt8 (Sqrt2 - x) = 11
    10·2 answers
  • 5.03+13.7+108 what is the answer an how do u solve it
    15·1 answer
  • HELP ASAP
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!