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
