Question

The common difference in an arithmetic sequence is –2 and the first term is 47. What is the 29th term?

a. –9
b. –11
c. 11
d. 18
If the first term of an arithmetic sequence is 4 and the third term is 18, what is the 23rd term?
a. 92
b. 116
c. 158
d. 161

Answer 1

the equation for the nth term of an arythmetic sequence is
an=a1+(n-1)d
an=nth term
a1=first term
n=n from the nth term
d=commno differnce


common difference is -2 and fist term is 47
what is n=29?
an=47+(n-1)(-2)
a29=47+(29-1)(-2)
a29=47+(28)(-2)
a29=47-56
a29=-9

answer is A


first erm is 4
third is 18
means
a1=4
a3=18
a3=a1+(3-1)d
a3=18=4+(3-1)d
18=4+(n-1)d
minus 4 both sides
14=(3-1)d
14=(2)d
divide both sides by 2
7=d
an=4+(n-1)7
what is 23th term
a23=4+(23-1)7
a23=4+(22)7
a23=4+154
a23=158

C


answers are A and C

Answer 2

An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).

The equation for an arithmetic sequence is

`A_(n)=A_(1)+(n-1)d`


`A_(n)` is the "n-th" number in the sequence (ex: is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 47 so
`A_(1)=47`
d=-2 because the question gives you that


`A_(n)=A_(1)+(n-1)d`

`A_(29)=47+(29-1)(-2)`

`A_(29)=47+(28)(-2)`

`A_(29)=47+-56`

`A_(29)=-9`

The answer is A. -9.



The answer is C. 158

For the second one, it gives you
`A_(1)=4` and
`A_{}=18`
You can use this to find d


`A_(n)=A_(1)+(n-1)d`

`A_(3)=4+(3-1)d`

`18=4+(3-1)d`

`18=4+2d`

`14=2d`

`7=d`

Now you can just solve using the equation normally.

`A_(n)=A_(1)+(n-1)d`

`A_(23)=4+(23-1)(7)`

`A_(23)=4+(22)(7)`

`A_(23)=4+154`

`A_(23)=158`

The answer is C. 158