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
Please help!!!! got to do this for math
Umnica [9.8K]

Answer:

11\sqrt{2}-5\sqrt{7}

7 0
3 years ago
Anyone know this??<br> pls help lol
Svetllana [295]
X={6,-10} that is the answer
3 0
3 years ago
A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is a hourly wage of $25. Optio
rodikova [14]
I love you euphorbia

4 0
2 years ago
Help Meeeeeeee!!!!!!!!
vesna_86 [32]

Answer: 1st one

Step-by-step explanation:

8 0
3 years ago
What is 7 3/10 as a percent
spin [16.1K]
730% is the answer!!
5 0
3 years ago
Read 2 more answers
Other questions:
  • Which is not a valid range? a1:a3, b1:b3 a1:a9 a1:f9 a1:f1?
    6·1 answer
  • Jennifer is playing with a die that has six faces. what is the likelihood that she will roll a four?
    8·2 answers
  • a company pays its employees a base salary of $1000 every other week. plus $30 for each sale. How many sales did the employee ha
    5·2 answers
  • A skydiver falls 144 ft in three seconds.how far does the skydiver fall per second
    14·2 answers
  • You toss a coin and spin a spinner. The spinner has four equal sections that are numbered from 1 to 4. Find the probability of g
    12·2 answers
  • Jesse finished the first race in two minutes and seven seconds. Tim finished 12 seconds faster than Jesse. Juan finish eight sec
    15·1 answer
  • Pavel hiked 6 miles on a camping trip . He hiked 3 times as many miles on his next camping trip. How many miles did pavel hike a
    13·1 answer
  • Evaluate Tan^-1 1<br> Easy points !!
    15·1 answer
  • If 640 acres is a square mile, and a mile is 1600 meters, how many square meters is an acre?
    9·1 answer
  • PLEASE HELP FAST Segment PR and segment QS are diameters of circle U. Find measure of arc ST
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!