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
VashaNatasha [74]
3 years ago
9

1. A recursive formula for the sequence 40, 30, 22.5, ... is *

Mathematics
1 answer:
romanna [79]3 years ago
7 0

Answer:

Step-by-step explanation:

Given the sequence

40, 30, 22.5.......

We want to find the general formula for the sequence.

Let find out if it is arithmetic progression or Geometric progression

Arithmetic progression have a common difference e.g 2,5,8,11...., you will notice they have a common difference of 3.

So, let apply this to the given sequence

40, 30, 22.5.......

d = T2 - T1

d = 30 - 40 = -10

d = T3 - T2

d = 22.5 - 30 = -7.5

So, the difference are not equal, then it is not AP.

Let check for GP, GP have common ratio

r = T2 / T1 = 30 / 40 = 0.75

r = T3 / T2 = 22.5 / 30 = 0.75

Since the common ratio are equal, then, the sequence is GP

The nth term of a G.P is given as

Un = ar^(n-1)

Where

a is first term

r is common ratio

From the given sequence

40, 30, 22.5.......

a = 40 and r = 0.75

Then,

Un = a•r^(n-1)

Un = 40 × 0.75^(n-1)

From indices

a^b / a^c = a^(b-c)

Un = 40 × 0.75ⁿ / 0.75

Un = 53.333 × 0.75ⁿ

Un = 160•0.75ⁿ / 3

That is the nth term at any point

But if we want to find the next term given we know the previous term

From G.P

U1 = a

U2 = U1 × r = ar

U3 = U2 × r = ar × r = ar²

So, in this case r = 0.75 = ¾

So, the previous term multiply by ¾ will give the next term

Then,

Un = U(n-1) × 0.75

Un = ¾ U(n-1)

Un is next term

U(n-1) is previous term

You might be interested in
WILL GIVE BRAINLIEST
Paul [167]
256.
EXPLANATION:

When you are using exponents, you are basically just doing repeated multiplication.

Whatever the exponent (smaller number is) is how many times you multiply the base number by itself.

So 4 ^4 is 4 x 4 x 4 x 4. (4 fours.)

So 4 x 4 x 4 x 4 is 256.
HAVE A GUD DAY
7 0
3 years ago
Compare. use <, > ,or = to complete the statement
8_murik_8 [283]
> hello there stranger
8 0
3 years ago
Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an
Murrr4er [49]

You'll have to c<span>ompass tip on A and draw a small ark with pencil approximately in the middle above AB line, now compass tip to point B and cross the ark you made previously.
Do the same on the opposite side without making any change to the compass 
Join the lines where crosses of arks on the both side meet and then ,it's done.</span>
8 0
3 years ago
On every 3rd day Ivan goes to the gym to exercise. Every 5th day Gavin goes to the gym to exercise. What is the first day Ivan a
Colt1911 [192]
You have to find the LCM (least common multiple) of both numbers.

3: 3, 6, 9, 12, 15
5: 5, 10, 15

ivan and gavin will be together at the gym on the 15th day.
8 0
3 years ago
Read 2 more answers
What is the volume of this shape?
snow_tiger [21]
D is the answer


6*10*3= 180 or


6*10 = 60*3 = 180
5 0
3 years ago
Read 2 more answers
Other questions:
  • Does the problem involve permutations or combinations? Do not solve. A club elects a president, vice-president, and secretary-tr
    10·1 answer
  • What is the area of the shaded region?<br> 3.3 km<br> 3 km
    11·1 answer
  • Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table.
    12·2 answers
  • Find the product of 987.2365 and 1,000.
    9·2 answers
  • The Ravens won twice as many games as they lost. They played 96 games. How many games did they win?
    8·1 answer
  • StartFraction 12 minus 3 y Over 2 EndFraction plus y StartFraction 2 y minus 4 Over y EndFraction for y = 3.
    13·2 answers
  • Howard is laying an oak wooden floor in his house. The measurements of the floor are 14.5 feet by 40 feet. The wood is packaged
    11·1 answer
  • For the following fraction ,tell whether you will add ,subtract, or multiply the exponents
    8·2 answers
  • A triangular prism. Rectangle A has a base of 14 meters and height of 8 meters. Rectangle B has a base of 14 meters and height o
    7·2 answers
  • Pls help 40 points pls
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!