Answer:
Explanation:
To complete the formula for the 32nd term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
Where:
an represents the nth term of the sequence,
a1 is the first term of the sequence,
r is the common ratio between consecutive terms, and
n is the position of the term in the sequence.
Given that 220 is equal to a32, we can substitute these values into the formula:
220 = a1 * r^(32-1)
Simplifying further:
220 = a1 * r^31
Now, let's solve for a1 and r using the second equation:
310 = a1 * r^31
From these two equations, we have a system of equations that we can solve simultaneously to find the values of a1 and r.
To find the 32nd term of the sequence, we can substitute the values of a1 and r into the formula:
a32 = a1 * r^(32-1)
Now, let's calculate this value using the given options:
a32 = 310 * (-228)^(32-1)
a32 = 310 * (-228)^31
Therefore, the complete formula for the 32nd term of the geometric sequence is:
220 = a1 * r^31
310 = a1 * r^31
a32 = 310 * (-228)^31