Question

Jia is skipping a rock across a pond. The sequence {4.2, 3.57, 3.0345, 2.5793, …} describes the height of the rock on each successive skip. Which explicit formula describes this geometric sequence?

Answer 1

Answer:

$u_n=4.2(0.85)^{n-1}$

Step-by-step explanation:

$u_1=4.2\\u_2=3.57\\u_3=3.0345\\u_4=2.5793$

Geometric formula sequence:   $u_n=ar^{(n-1)}$

(where $a$ is the first term of the sequence and $r$ is the common ratio)

To find the common ratio, divide one of the terms by the previous term:

$r=\frac{u_2}{u_1} =\frac{3.57}{4.2} =0.85$

From inspection, $a=4.2$

Therefore, $u_n=4.2(0.85)^{n-1}$

Answer 2

Answer:

Answer:

${ \boxed{\tt {a _{n} = 4.94\times 0.85{}^{n} }}}$

Step-by-step explanation:

» General explicit formula for geometric sequence:

${ \tt{a _{n} = ar {}^{n - 1} }}$

• a → first term
• a_n → nth term
• r → common ratio

» In the sequence given;

• n → 4
• a_1 → 4.2
• r → 4.2/3.57 → 17/20

${ \tt{a _{n} = 4.2 \times {( \frac{17}{20}) }^{n- 1} }} \\ \\ { \tt{{a _{n} = 4.2 \times ( \frac{17}{20}) {}^{n} \times ( \frac{17}{20}) {}^{ - 1} }}} \\ \\ { \tt{a _{n} = 4.2 \times ( \frac{17}{20}) {}^{n} \times \frac{20}{17} }} \\ \\{ \tt {a _{n} = 4.94\times 17/20 {}^{n} }}$