+637 A geometric sequence has 400 terms. The first term is 1600 and the common ratio is $-\frac{1}{2}.$ How many terms of this sequence are greater than 1000?
+1234
A geometric sequence has 400 terms.
The first term is 1600 and the common ratio is –1/2.
How many terms of this sequence are greater than 1000?
There won't be that many so let's just count them.
1600 • –1/2 = –800
–800 • –1/2 = 400
400 • –1/2 = –200
–200 • –1/2 = 100
100 • –1/2 = –50
–50 • –1/2 = 25
The numbers are just going to keep dwindling away.
It's pretty obvious that there is only one term in this
sequence greater than 1000, i.e., the first one 1600.
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