1. what is the recursive rule for the sequence?

−22.7, −18.4, −14.1, −9.8, −5.5, 
an=an+1+4.3 , where a1=−22.7

an=an−1−4.3 , where a1=−22.7

an=an−1+4.3 , where a1=−22.7

an=an+1−4.3 , where a1=−22.7

2. which answer is the explicit rule for the sequence 14.5, 11, 7.5, 4, 0.5,  ?

an=18−3.5n

an=18+3.5n

an=14.5−3.5n

an=14.5+3.5n


3. he explicit rule for a sequence is given.

an=3n+1

what is the recursive rule for the sequence?

a1=3;  an=an−1+1

a1=4;  an=an−1+1

a1=1;  an=an−1+3

a1=4;  an=an−1+3

4. a supermarket finds that the number of boxes of a new cereal sold increases each week. in the first week, only 16 boxes of the cereal were sold. in the next week, 33 boxes of the cereal were sold and in the third week 50 boxes of the cereal were sold. the number of boxes of cereal sold each week represents an arithmetic sequence.

what is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?

an=17n+1

an=17n−1

an=17n+33

an=17n−33

Answer 1: The correct option is C ). A(n)=A(n-1)+4.3 , where A(1)=(−22.7)

Answer 2: The correct option is A ). A(n)=18−3.5n

Answer 3: The correct option is D ). A(1)=4; A(n)=A(n−1)+3

Answer 4: The correct option is B ). A(n)=17n-1

Step-by-step explanation:

An arithmetic sequence is given by a,a+d,a+2da+(n-1)d

a is first term of sequence and d is interval of sequence

Where A(n)=a+(n-1)d

The recursive rule for the sequence is given by

A(n)=A(n-1)+d

The explicit rule for the sequence is given by

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

Answer 1:

Given sequence is −22.7, −18.4, −14.1, −9.8, −5.5

One comparing the sequence

we get, a=(-22.7) and a+d=(-18.4)

Interval of sequence d=(a+d)-(a)

d=(-18.4)-(-22.7)

d=4.3

The recursive rule for the sequence is given by

A(n)=A(n-1)+d

A(n)=A(n-1)+4.3

The correct option is C ). A(n)=A(n-1)+4.3 , where A(1)=(−22.7)

Note : The correct option is D is correct, if we write recursive rule as

A(n)=A(n+1)-d

A(n)=A(n+1)-4.3

Answer 2:

Given sequence is 14.5, 11, 7.5, 4, 0.5

One comparing the sequence

we get, a=14.5 and a+d=11

Interval of sequence d=(a+d)-(a)

d=(11)-(14.5)

d=(-3.5)

The explicit rule for the sequence is given by

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

A(n)=14.5+(n-1)(-3.5)

A(n)=14.5-3.5n+3.5

A(n)=18-3.5n

The correct option is A ). A(n)=18−3.5n

Answer 3:

Given explicit rule for a sequence is A(n)=3n+1

For A(1):

A(n)=3n+1

A(1)=3(1)+1=4

For A(n-1):

a(n)=3n+1

A(n-1)=3(n-1)+1

A(n-1)=3n-3+1

A(n-1)=3n-2

The recursive rule for the sequence is given by

A(n)=A(n-1)+d

3n+1=3n-2+d

d=3

The recursive rule for the sequence is A(n)=A(n-1)+3

The correct option is D ). A(1)=4; A(n)=A(n−1)+3

Answer 4:

A supermarket finds that the number of boxes of a new cereal sold increases each week.

In the first week, 16 boxes of the cereal were sold

In the second week, 33 boxes of the cereal were sold

In the third week, 50 boxes of the cereal were sold

An arithmetic sequence is given by a,a+d,a+2da+(n-1)d

Here,

a=16 and a+d=33

Hence d=(a+d)-(a)=33-16=17

The explicit rule for the sequence is given by

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

A(n)=16+(n-1)17

A(n)=16+17n-17

A(n)=17n-1

The correct option is B ). A(n)=17n-1

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