How do you write the explicit formula for the sequence 0.5,-0.1,0.02,-0.004...?

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How do you write the explicit formula for the sequence 0.5,-0.1,0.02,-0.004...?

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Answer 1 · 2016-03-09T10:10:27

Explicit formula for the sequence's $n^{t h}$ $n^(th)$ term is $0.5 \times {(- \frac{1}{5})}^{n - 1}$ $0.5xx(-1/5)^(n-1)$

Explanation:

The sequence ${0.5, - 0.1, 0.02, - 0.004, . .}$ ${0.5,-0.1,0.02,-0.004,..}$ is a geometric series of the type ${a, a, ar^2, ar^3,....}$ , in which $a$ - the first term is $0.5$ and ratio $r$ between a term and its preceding term is $-1/5$ .

As the $n^(th)$ term and sum up to $n$ terms of the series ${a, a, ar^2, ar^3,....}$ is $ar^(n-1)$ and $(a(1-r^n))/(1-r)$ (as $r<1$ - in case $r>1$ one can write it as $(a(r^n-1))/(r-1)$ .

As such $n^(th)$ term of the given series ${0.5,-0.1,0.02,-0.004,..}$ is $0.5xx(-1/5)^(n-1)$

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How do you write the explicit formula for the sequence 0.5,-0.1,0.02,-0.004...?

1 Answer

Explanation:

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