What is the recursive formula for geometric sequence #{2,10,50,250,..........}#?

Answer 1

The recursive formula for the geometric sequence {2, 10, 50, 250, ...} is given by (a_{n+1} = 5 \times a_n) for (n \geq 1), where (a_1 = 2).

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Answer 2

Savannah Anderson

Recursive formula is #a_n=a_(n-1)xx1/5#

In a Geometric sequence, the ratio of each term to its preceding term is always constant and is known as common ratio #r#. Here, we observe that the ratios #50/250=10/50=2/10# are all #1/5#. Hence common ratio is #1/5#.

Recursive formula is the formula, which generates subsequent term from its preceding term.

For example #a_n# as a function of #a_(n-1)#.

It is apparent that in the given Geometric sequence recursive formula is #a_n=a_(n-1)xx1/5#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.