Question

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

Answer 1

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

Answer 2

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