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Elina [12.6K]
3 years ago
6

⎧

Mathematics
1 answer:
MrRissso [65]3 years ago
7 0

Answer:

f(n)=-5-3n

Step-by-step explanation:

Given the recursive formula of a sequence

f(1)=−8

f(n)=f(n−1)−3

We are to determine an explicit formula for the sequence.

f(2)=f(2-1)-3

=f(1)-3

=-8-3

f(2)=-11

f(3)=f(3-1)-3

=f(2)-3

=-11-3

f(3)=-14

We write the first few terms of the sequence.

-8, -11, -14, ...

This is an arithmetic sequence where the:

First term, a= -8

Common difference, d=-11-(-8)=-11+8

d=-3

The nth term of an arithmetic sequence is determined using the formula:

T(n)=a+(n-1)d

Substituting the derived values, we have:

T(n)=-8-3(n-1)

=-8-3n+3

T(n)=-5-3n

Therefore, the explicit formula for f(n) can be written as:

f(n)=-5-3n

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1-(-5)/7-2

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1

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again

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3 years ago
What part of 3 dollars are 25 nickels
Agata [3.3K]

Answer:

25 nickles are 5/12ths of a dollar

Step-by-step explanation:

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6 0
3 years ago
Suppose A is n x n matrix and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row
vovangra [49]

Answer:

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

4 0
3 years ago
Find the median of the following set of data:
Troyanec [42]

Answer:

b

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.

Arrange the data in ascending order

48, 52, 54, 57, 57, 57, 61, 61, 65

                          ↑

The median of the data set is 57 → b

3 0
3 years ago
A summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. which values correctly comp
Lapatulllka [165]

The values which completes the table regarding summer camp is option b which is a=15,b=7, c=5, d=10, e=12.

Given that there are 32 campers, 22 of them can swim, 20 play softball and 5 do not play softball or swim.

We have to find the values of a,b,c,d,e so that we can complete the table.

Table is a combination of rows and columns. In our case the third row and third column shows the total.

from the table we can write that 22+d=32-----------1

so d=32-22

=10

d=10

c+5=d-----------2

c=10-5=5

c=5

a+c=20------------------3

a+5=20

a=20-5

a=15

a+b=22--------------3

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20+e=32----------4

e=32-22

e=10.

Hence the values which completes the table is a=15,b=7, c=5, d=10,  e=12.

Learn more about table at brainly.com/question/12151322

#SPJ4

Question is incomplete as it should include figure showing table of values.

6 0
2 years ago
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