What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?
1 answer:
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Answer:
Step-by-step explanation:
So we have the expression:
For both the numerator and the denominator, factor out a 5:
The term in the numerator can be factored. This is the difference of two squares pattern:
Both layers have a 5(x+2). Cancel them, Since we know that x <em>cannot</em> be -2, we can safely do so:
And we're done!
Notes:
If we weren't told that x ≠ -2, then we cannot divide them because if x <em>did</em> equal -2, the equation would be undefined. However, since we were given that, we can simplify.
However, even if we weren't given x ≠ -2, we can <em>still</em> simplify, but we need to add the restraint ourselves. This must be done, or else the equation won't be correct.