QuestionFind the common ratio of the geometric sequence where $\mathrm{a}_{1}=1$ and $\mathrm{a}_{9}=25$ .

Studdy Solution

STEP 1

Assumptions1. The sequence given is a geometric sequence. The first term of the sequence is33. The sequence follows a pattern where each term is multiplied by a common ratio

STEP 2

In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. We can find the common ratio by dividing any term in the sequence by the term before it.
$Common\, ratio = \frac{a_{n}}{a_{n-1}}$

STEP 3

Now, plug in the given values for the first and second term of the sequence to calculate the common ratio.
$Common\, ratio = \frac{6}{3}$

STEP 4

Calculate the common ratio.
$Common\, ratio = \frac{6}{3} =2$ The common ratio of the geometric sequence is2.

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