Question

Consider the sequence an = 9(0.4)n. which rule defines sn? sn = 6(0.4n) sn = 9(0.4n) sn = 6(1 – 0.4n) sn = 9(1 – 0.4n)

Answer 1

The rule that the defines the sum Sn is $S_n =\frac{9 * (1 - r^n )}{0.6}$

How to determine the expression for Sn?

The formula of the sequence is given as:

an = 9(0.4)^n

The above means that:

• The first term, a = 9
• Common ratio, r = 0.4

The sum Sn is then represented as:

$S_n =\frac{a(1 - r^n )}{1 - r}$

So, we have:

$S_n =\frac{9 * (1 - r^n )}{1 - 0.4}$

Evaluate the difference and divide

$S_n =\frac{9 * (1 - r^n )}{0.6}$

Hence, the rule that the defines the sum Sn is $S_n =\frac{9 * (1 - r^n )}{0.6}$

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