How do you write the first five terms of the geometric sequence $a_{1} = 5, r = - \frac{1}{10}$ $a_1=5, r=-1/10$ ?

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Answer 1 · 2017-04-21T08:06:39

$5 - 0.5, 0.05, - 0.005, 0.0005$ $" "5" "-0.5," "0.05," "-0.005," "0.0005$

The General term is $T_{n} = a n^{n - 1}$ $T_n = an^(n-1)$

Option 1.: Let $n = 1, 2, 3, 4, 5$ $n = 1,2,3,4,5$ and calculate each term.

Option 2: Multiply one term by $- \frac{1}{10}$ $-1/10$ to get the next.
This seems the easier option.

$5 \times - \frac{1}{10} = - 0.5$ $5 xx -1/10= -0.5$

$- 0.5 \times - \frac{1}{10} = 0.05$ $-0.5 xx-1/10 = 0.05$ and so on,

This gives: $5 - 0.5, 0.05, - 0.005, 0.0005$ $" "5" "-0.5," "0.05," "-0.005," "0.0005$

Notice the sign changes each time.

How do you write the first five terms of the geometric sequence a_1=5, r=-1/10a1=5,r=−110a_1=5, r=-1/10?