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How do you write the first five terms of the geometric sequence $a_{1} = 2, r = \frac{x}{4}$ $a_1=2, r=x/4$ ?

1 Answer

Jun 6, 2017

$2, \frac{x}{2}, \frac{x^{2}}{8}, \frac{x^{3}}{32}, \frac{x^{4}}{128}$ $2,x/2,x^2/8,x^3/32,x^4/128$

Explanation:

multiply the previous term by the common ratio $r$ $" "r$

$a_{1} = 2$ $a_1=2$

$a_{2} = a_{1} \times \frac{x}{4} = 2 \times \frac{x}{4} = \frac{x}{2}$ $a_2=a_1xxx/4=2xxx/4=x/2$

$a_{3} = \frac{x}{2} \times \frac{x}{4} = \frac{x^{2}}{8}$ $a_3=x/2xxx/4=x^2/8$

$a_{4} = \frac{x^{2}}{8} \times \frac{x}{4} = \frac{x^{3}}{32}$ $a_4=x^2/8xxx/4=x^3/32$

$a_{5} = \frac{x^{3}}{32} \times \frac{x}{4} = \frac{x^{4}}{128}$ $a_5=x^3/32xxx/4=x^4/128$

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