Common ratio

If 200 units of a commodity are consumed in a first year, and if the annual rate of increase in consumption is 5%

(a) what amount is consumed in the 8th year;
(b) in the first 15 years?

Correct answer:

a₈ =  281.4201
s₁₅ =  4315.7127

Step-by-step explanation:

$$\begin{gathered} a_1=200 \\ q=5\mathrm{\%}=1+{\displaystyle \frac{5}{100}}=1.05 \\ {a}_8=a_1\cdot q^{8-1}=200\cdot 1.05^{8-1}=281.4201 \end{gathered}$$

$s_{15}=a_1\cdot {\displaystyle \frac{q^{15}-1}{q-1}}=200\cdot {\displaystyle \frac{1.05^{15}-1}{1.05-1}}=4315.7127$

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