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
3. Given f(x)=-2(5)<br> Find f (4)
zzz [600]

Answer:

f

(

x

)

=

2

, means, whatever be the value of

x

, f(x)=2#.

∴

f

(

−

4

)

=

2

.

6 0
2 years ago
15.<br> Find the slope of a line perpendicular to 2y=-6x+8<br><br> 2/3<br> 6<br> 1/3<br> -3/2
Yakvenalex [24]
The slope of the given line is found from the coefficient of x after dividing the equation by 2.
.. y = -3x +4
The given line has slope -3.
A perpendicular line will have a slope that is the negative reciprocal of this:
.. -1/(-3) = 1/3

This corresponds to your 3rd choice.

4 0
3 years ago
letters cost $1 each to send in the mail and packages cost $5 each the equation x + 5y = 25 describes how many letters and packa
Vlada [557]

Answer:

y is the packages in the equation

4 0
3 years ago
Determine the quotient, g(x), and remainder, r(x) when
lianna [129]

Answer:

Quotient : 2x^2 + 5x + 3

Remainder : x + 3

Step-by-step explanation:

I've attached the solution

5 0
3 years ago
Giving 20 points and please help
vlabodo [156]

Hello,

Question- In the picture

Answer- The correct answer is A Because all you do is multiply buy 2 thats how simple it is.

Important- If my answer was enough to help you understand please mark me as brainliest thank you and have the best day ever!


5 0
3 years ago
Other questions:
  • Tickets for a minor league baseball game for an adult and two children cost a total of $21 the adult ticket is three dollars mor
    12·1 answer
  • A professional football field is 160 feet wide. What is the width in yards?
    11·2 answers
  • Algebra 2 Grade 11
    8·1 answer
  • PLEASE ANSWER ASAP
    10·1 answer
  • A family of 8 mice move into your barn. After 3 months, there are now 51 mice. At 8 months, how many mice will you have in your
    14·1 answer
  • Please help meeeeeeeeeeeeeeeeee
    13·2 answers
  • a 36 foot is attached from the top of a pole to a bracket that is 9 feet from the base of the pole how tall is the pole?
    9·1 answer
  • There are 5,000 books in the​ town's library. Of​ these, 4,700 are fiction. To find the percent of the books that are​ fiction,
    5·2 answers
  • A car dealer offers a 15% discount off the list price x of any car on the lot. At the same time, the manufacturer offers a 1000$
    8·1 answer
  • The surface area of a right square pyramid is 50 square inches. If the sides of the base and the slant height of the pyramid are
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!