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In a geometric sequence where the terms always increase, the common ratio ( r ) must be greater than 1. This means that each term is obtained by multiplying the previous term by this positive ratio. For example, if the first term is ( a ) and the common ratio is ( r ), the sequence would look like ( a, ar, ar^2, ar^3, \ldots ) with each term growing larger than the last. Thus, the sequence exhibits exponential growth as long as the common ratio remains above 1.
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Do the terms of a geometric sequence increase as it proceeds?
yes
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
What does geometric sequence?
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
What is the answer if you insert 3 terms between 2 and 32 by geometric sequence?
The terms are: 4, 8 and 16
What is the geometric sequence formula?
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
