Answer and step-by-step explanation:
To create the sequence, let's find the common difference to find the missing term which is the second term.
Use the formula for an arithmetic sequence:
An = A1 + (n - 1)d
where
An is the nth term,
A1 is the first term,
n is the number of terms, and
d is the common difference.
Let's substitute the given values to the formula. Then simplify.
An = A3 = 1/2
A1 = 12
n = 3
1/2 = 12 + (3 - 1)d
1/2 = 12 + 2d
1/2 - 12 = 2d
-23/2 = 2d
-23/2 /2 = 2d/2
-23/4 = d
Thus, the common difference is -23/4.
Let's find the second term of the sequence by subtituting the formulas again. Then simplify.
A2 = 12 + (2 - 1)(-23/4)
A2 = 12 + (1)(-23/4)
A2 = 12 + (-23/4)
A2 = 25/4
Therefore, the sequence is 12, 25/4, 1/2.
Proof:
Check if the given third term will be the same after you add the common difference to the second term.
A2 + d = A3
25/4 + (-23/4) = 1/2
1/2 = 1/2
Therefore, it satisfies the given conditions and the sequence is correct.
