Answer: 1,953,125
This is one single value and it is just a bit under 2 million.
Or more accurately, it's a bit over 1.9 million.
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Step-by-step explanation:
- a = 5 = first term
- r = -5 = common ratio
Note that dividing any term by its previous term gets us the common ratio
- r = term2/term1 = -25/5 = -5
- r = term3/term2 = 125/(-5) = -5
The r value must stay the same the entire time, or else the sequence isn't geometric.
The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)
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To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.
If we tried n = 2 for instance, then we find the 2nd term is
5(-5)^(n-1) = 5(-5)^(2-1) = -25
which matches what your teacher gave you. I'll let you verify the other terms.
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The last thing we need to do is plug in n = 9 and simplify
5(-5)^(n-1)
5(-5)^(9-1)
5(-5)^8
5(390625)
1,953,125 this is one single value (rather than 3 separate values)