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
Sunny_sXe [5.5K]
3 years ago
5

Find an explicit form f(n) of the arithmetic sequence where the 2nd term is 25 and the sum of the 3rd term and 4th

Mathematics
1 answer:
Westkost [7]3 years ago
7 0

Answer:f(n) = 12n + 1

Step-by-step explanation:

Since it is an arithmetic sequence, the general formula for nth term is given as

\\f(n) = a + ( n-1)d , where a is the first term, n is the number of terms and d is the common difference.

\\Given from the question

\\Second term  is 25 , which means that

a + d = 25  

\\Also given , the sum of third and fifth term is 86, which means

\\a + 2d + a + 3d = 86

\\2a + 5d = 86

\\Combining the two equations , we have

\\a + d = 25 ………….. I

\\2a + 5d = 86………..II  

\\Using substitution method  to solve the resulting simultaneous equation

\\From equation I make a the subject of the formula, which gives

\\ a = 25 – d…………………. III

\\Substitute the value of a into equation II , we have

\\2 ( 25 – d) + 5d = 86

\\Expanding

\\50 + 2d + 5d = 86

\\50 + 3d = 86

\\Collect the like terms

\\3d = 86 – 50

\\3d = 36

\\d = 12

\\substitute the value of d into equation III, we have

\\a = 25 – 12

\\a = 13

\\Since we have gotten the value of a and b , we will substitute into the general formula for the nth term

\\f(n) = a + ( n-1)

\\f(n) = 13 + (n-1)12

\\Expanding

\\f(n) = 13+ 12n -12

f(n) =12n + 1

\\Therefore the explicit form f(n) of the arithmetic sequence is f(n) =12n + 1

You might be interested in
What makes a graph a proportional relationship?
saw5 [17]

Answer:The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y = kx, where k is a constant ratio. You can tell that the relationship is directly proportional by looking at the graph.



Step-by-step explanation:


8 0
3 years ago
Help with comparisons?
notsponge [240]
I think 1 is =
2 is =
3 is >
4 is =
5 is =

But I am really not good at math, so I hope I got them right for you!

-Twix
3 0
3 years ago
What is 65% of 80 ??????????????
bazaltina [42]

Answer:

Step-by-step explanation:

65% of 80 is

65*80/100=52

4 0
3 years ago
Read 2 more answers
How do i solve this step by step? <br><br> 3( q – 3 ) = 6
mote1985 [20]

Answer:

3q-9=6

3q=9+6

3q=15

q=5

7 0
3 years ago
Find the circumference of circle if the diameter is 7.8cm<br>​
olasank [31]

Answer:

24.5

Step-by-step explanation:

the radius is half of a diameter

so the radius is 3.9

24.5 = 2πr= 2 * π * 3.9 ≈ 24.504

4 0
3 years ago
Other questions:
  • Suppose you had to find 4 x 57. How are the expanded algorithm and the standard algorithm alike? And how are they different?
    14·1 answer
  • How can you use absolute value to represent a negative number in a real world solution
    13·1 answer
  • The dot plots below show the distances traveled by two groups of bikers: Two dot plots are labeled Group A and Group B. The hori
    5·2 answers
  • The two polygons below are similar.
    6·2 answers
  • A room has a floor area of 120 square feet and a height of 8 feet. What is the volume of the room?
    15·1 answer
  • Aspirin is sold in boxes of 24 for $3.69, 50 for $5.49, 100 for $8.29, and 150 for $11.99. Which box has the best unit rate.
    14·1 answer
  • Has anyone taken the math kangaroo competition
    15·1 answer
  • Simplify the following expression and write in standard form: 3 x (6y - 4y + 5x) PLEASE HELP
    14·1 answer
  • −8x+6−2=−12<br> what is x?
    5·2 answers
  • Factor 13
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!