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
[tex]A_{n}=A_{1}+(n-1)d[/tex]
[tex]A_{n}[/tex] 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 [tex]A_{1}=47[/tex]
d=-2 because the question gives you that
[tex]A_{n}=A_{1}+(n-1)d[/tex]
[tex]A_{29}=47+(29-1)(-2)[/tex]
[tex]A_{29}=47+(28)(-2)[/tex]
[tex]A_{29}=47+-56[/tex]
[tex]A_{29}=-9[/tex]
The answer is A. -9.
The answer is C. 158
For the second one, it gives you [tex]A_{1}=4[/tex] and [tex]A_{}=18[/tex]
You can use this to find d
[tex]A_{n}=A_{1}+(n-1)d[/tex]
[tex]A_{3}=4+(3-1)d[/tex]
[tex]18=4+(3-1)d[/tex]
[tex]18=4+2d[/tex]
[tex]14=2d[/tex]
[tex]7=d[/tex]
Now you can just solve using the equation normally.
[tex]A_{n}=A_{1}+(n-1)d[/tex]
[tex]A_{23}=4+(23-1)(7)[/tex]
[tex]A_{23}=4+(22)(7)[/tex]
[tex]A_{23}=4+154[/tex]
[tex]A_{23}=158[/tex]
The answer is C. 158
