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Answer:
Step-by-step explanation:
First, write some equations so we can figure out the common ratio and the initial term. The standard explicit formula for a geometric sequence is:
Where xₙ is the nth term, a is the initial value, and r is the common ratio.
We know that the second and fifth terms are -21 and 567, respectively. Thus:
Substitute them into the equations:
And:
To find a and r, divide both sides by a in the first equation:
And substitute this into the second equation:
Simplify:
The as cancel out. (-21)^4 is 194481:
Cross multiply:
Take the cube root of both sides:
Therefore, the initial value is 7.
And the common ratio is (going back to the equation previously):
Thus, the common ratio is -3.
Therefore, the equation is: