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# geometric sequence

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Find the 7th term of sqrt(2), sqrt(10), 5*sqrt(2), ...

May 3, 2022

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I am assuming this is a geometric sequence because of the title of the post.

You can find the common ratio, by dividing the second term by the first term. $$\text{Common ratio} = \dfrac{\sqrt{10}}{\sqrt2} = \sqrt{\dfrac{10}2} = \sqrt5$$.

Since the nth term of a geometric sequence is $$ar^{n - 1}$$ where a is the first term and r is the common ratio, you can now substitute a = sqrt(2), r = sqrt(5), n = 7 to get the value of the 7th term.

May 3, 2022