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
WINSTONCH [101]
3 years ago
15

In an arithmetic sequence, a17 = -40 and

Mathematics
2 answers:
Viktor [21]3 years ago
5 0

Answer:

Tn = 2Tn-1 - Tn-2

Step-by-step explanation:

Before we can generate the recursive sequence, we need to find the nth term of the given sequence.

nth term of an AP is given as:

Tn = a+(n-1)d

If a17 = -40

T17 = a+(17-1)d = -40

a+16d = -40 ...(1)

If a28 = -73

T28 = a+(28-1)d = -73

a+27d = -73 ...(2)

Solving both equations simultaneously using elimination method.

Subtracting 1 from 2 we have:

27d - 16d = -73-(-40)

11d = -73+40

11d = -33

d = -3

Substituting d = -3 into 1

a+16(-3) = -40

a - 48 = -40

a = -40+48

a = 8

Given a = 8, d = -3, the nth term of the sequence will be

Tn = 8+(n-1) (-3)

Tn = 8+(-3n+3)

Tn = 8-3n+3

Tn = 11-3n

Given Tn = 11-3n and d = -3

Tn-1 = Tn - d... (3)

Tn-1 = 11-3n +3

Tn-1 = 14-3n

Tn-2 = Tn-2d...(4)

Tn-2 = 11-3n-2(-3)

Tn-2 = 11-3n+6

Tn-2 = 17-3n

From 3, d = Tn - Tn-1

From 4, d = (Tn - Tn-2)/2

Equating both common difference

(Tn - Tn-2)/2 = Tn - Tn-1

Tn - Tn-2 = 2(Tn - Tn-1)

Tn - Tn-2 = 2Tn-2Tn-1

2Tn-Tn = 2Tn-1 - Tn-2

Tn = 2Tn-1 - Tn-2

The recursive formula will be

Tn = 2Tn-1 - Tn-2

Katen [24]3 years ago
3 0

Answer:

The difference between the given terms is

–73 – (–40) = –33.

The difference between the term numbers is 28 – 17 = 11.

Dividing –33 / 11 = –3.

The common difference is –3.

The recursive formula is the previous term minus 3, or an = an – 1 - 3 where a17 = -40.

You might be interested in
Use the elimination method to solve the system of equations -x+5y=-4 and 4x+3y=16
jenyasd209 [6]

Answer:

A.(4,0)

Step-by-step explanation:

APEX

7 0
3 years ago
Determine whether the given value is a solution of the equation. write Yes or No.
givi [52]

Answer:

  1. yes 3.no 5.yes 7.there is no s in the equation

6 0
3 years ago
Simplify the following rational expression and express in expanded form.
VladimirAG [237]

Answer:

D m =  -\frac{3}{8}

Step-by-step explanation:

factor the expressions in the denominator and the numerator to simplify the expression:

=> \frac{2(-2m + 1)(2m - 1)}{2(2m - 1)(8m + 3)}

=> -\frac{2m + 1}{8m + 3}

to make a fraction undefined, the numerator should be 0, thus, we substitute the values of m from the options into the denominator to make the denominator equals to 0:

=> -\frac{2m + 1}{8(-\frac{3}{8} ) + 3} = -\frac{2m + 1}{-3 + 3} = -\frac{2m + 1}{0}

in this case, the values of m from option D make the denominator of the fraction equals 0.

6 0
3 years ago
The circumference of the
Tju [1.3M]

To the nearest inch it'll be

d×3.14=63

= 20 inches

8 0
3 years ago
Plot three points and draw the line that has the following parametric equations:
juin [17]
Y = -3x  + 6

y - 6 = -3x

-1/3 y + 2 = x

z = x  -3

z = -1/3 y + 2 -3 = -1/3  y  - 1 

set z = 0

-1/3 y = 1

y = -3

set y = 0

z = - 1 

7 0
3 years ago
Read 2 more answers
Other questions:
  • A model predicts the profit, p of a company as p(x) = x3 – 3x2 – 16x + 48, where p is in thousands of dollars and x is number of
    7·1 answer
  • Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth
    14·1 answer
  • What is another name for 23 ten thousands?
    6·1 answer
  • Line AB contains points A(4, 5) and B(9,7). What is the slope of AB?
    6·2 answers
  • 2 x - 5 ( 5 - x ) = 24
    5·1 answer
  • 4d to the third power-10 in verbal expression
    6·1 answer
  • Solve using equivalent ratios.
    10·1 answer
  • Write the equation in standard form of the quadratic that has a root of (3,0) and a vertex at (1,-4), then list out the values o
    11·1 answer
  • Hey guys could someone please help me?
    8·1 answer
  • What is the measure of y
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!