What is the 8th term of the geometric sequence 4, -20, 100?
1 Answer
Explanation:
Whenever looking at sequences, you have to attempt to find a common factor between the members of that sequence, be it the difference between them, a common divisor, a common multiplier, etc. In this case, we can see that if we divide each member by the previous one, we get a the same number:
So our sequence, starting at 4 is represented by the following recursive equation:
This is fine if we like calculating each previous member in order to get to whatever number in the sequence we need, but there is a better way (specially if the question asks for the 15th member or something higher).
Let's look at each calculation as a full equation:
Notice that at each step all we're doing is adding a multiplication by
Also note that this would even allow you to calculate the first step as any number raised to