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
Explanation:
An arithmetic sequence is given by a,a+d,a+2d.......a+(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+2d.......a+(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