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Yes, the common ratio in a geometric progression can be 1. In a geometric progression, each term is obtained by multiplying the previous term by a constant factor, known as the common ratio. When the common ratio is 1, each term is equal to the previous term, resulting in a sequence of repeated values. This is known as a constant or degenerate geometric progression.
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What is the sum of the first 15 terms of an arithmetic?
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
What is the pattern for a half a quarter and an eighth?
It's a geometric progression with the initial term 1/2 and common ratio 1/2. The infinite sum of the series is 1.
Condition for an infinite geometric series with common ratio to be convergent?
The absolute value of the common ratio is less than 1.
How do you find the common ratio in a geometric sequence?
Divide any term in the sequence by the previous term. That is the common ratio of a geometric series. If the series is defined in the form of a recurrence relationship, it is even simpler. For a geometric series with common ratio r, the recurrence relation is Un+1 = r*Un for n = 1, 2, 3, ...
What does Geometric Series represent?
A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)
