# Thread: Series and Sequence question

1. ## Series and Sequence question

Hi,

ThanksScreen Shot 2018-01-19 at 8.33.45 pm.pngScreen Shot 2018-01-19 at 8.34.06 pm.png

2. ## Re: Series and Sequence question

The question is somewhat ambiguously worded but I will assume the meaning to be "decreasing by 5% of the previous year's population".

Use the formula for geometric sequences.

Let $T_n$ be the population, expressed as a percentage of the original, at the start of the $n$th year (be careful with wording).

$T_n = ar^{n-1}$

$a = 1$

$r = 0.95$ (decreasing by 5% is the same as taking 95%)

You can do the first question with simple substitution. The other two can be done with a substutition and then rearranging to make $n$ the subject (logarithms will be required).

3. ## Re: Series and Sequence question

Thank you

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