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Q: In a geometric sequence where r and gt 1 the terms always increase.?

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FALSE (Apex)

yes

Yes, that's what a geometric sequence is about.

A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.

Ratio

A static sequence: for example a geometric sequence with common ratio = 1.

It is 4374

I expect that you mean the formula for calculating the terms in a geometric sequence. Please see the link.

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.

The terms are: 4, 8 and 16

They are 14, 42, 126, 378 and 1134.

It is a constant, other than 0 or 1.

No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...

a, ar, ar^2 and ar^3 where a and r are constants.

1 to 4

Un = 4*3n-1 S9 = 39364

It could be -3 or +3.

An arithmetic sequence does not have a constant rate of increase or decrease between successive terms, so it cannot be called anything!The constant increase or decrease is called the common difference.

What is the sum of the first 27 terms of the geometric sequence -3, 3, - 3, 3, . . . ?

The sequence is arithmetic if the difference between every two consecutive terms is always the same.

Right angle and rectangle are geometric terms.

An arithmetic series is the sequence of partial sums of an arithmetic sequence. That is, if A = {a, a+d, a+2d, ..., a+(n-1)d, ... } then the terms of the arithmetic series, S(n), are the sums of the first n terms and S(n) = n/2*[2a + (n-1)d]. Arithmetic series can never converge.A geometric series is the sequence of partial sums of a geometric sequence. That is, if G = {a, ar, ar^2, ..., ar^(n-1), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.

a+a*r+a*r^2+...+a*r^n a = first number r = ratio n = "number of terms"-1

The formula to find the sum of a geometric sequence is adding a + ar + ar2 + ar3 + ar4. The sum, to n terms, is given byS(n) = a*(1 - r^n)/(1 - r) or, equivalently, a*(r^n - 1)/(r - 1)

Geometric Sequences work like this. You start out with some variable x. Your multiplication distance between terms is r. Your second term would come out to x*r, your third x*r*r, and so on. If there are n terms in the sequence, your final term will be x*r^(n-1).

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