Write the explicit formula for the geometric sequence

Ответ:

emmaja121003

01.01.2022

Mathematics

Option C is correct.

$a_n =4 \cdot 5^{n-1}$

Explanation:

Explicit formula for the geometric sequence is given by:

$a_n =a_1 \cdot r^{n-1}$

where r is the common ratio

Given the recursive formula for geometric sequence:

a_1 = 4

$a_n =5 \cdot a_{n-1}$

For n =2

$a_2 = 5 \cdot a_{2-1}$

$a_2 = 5 \cdot a_1$

⇒ $a_2 = 5 \cdot 4 = 20$

For n =3

$a_3= 5 \cdot a_{3-1}$

$a_3= 5 \cdot a_{2}$

⇒ $a_3= 5 \cdot 20 = 100$

Common ratio(r):

$\frac{a_2}{a_1} = \frac{20}{4} = 5$

$\frac{a_3}{a_2} = \frac{100}{20} = 5$

⇒ r = 5

Therefore, the explicit formula for the geometric sequence represented by the recursive formula is:

$a_n =4 \cdot 5^{n-1}$

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Ответ:

naomirice24

19.03.2023

Mathematics

$212.40

Step-by-step explanation:

180+ (180* 18%)= Total Cost

180+ 32.40= Total Cost

212.40= Total Cost

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Write the explicit formula for the geometric sequence represented by the recursive formula.
a1 = 4
an = 5 · an-1
a) an = 4 · 5n
b) an = 5 · 4n
c) an = 4 · 5n-1
d) an = 5 · 4n-1

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Write the explicit formula for the geometric sequence represented by the recursive formula. a1 = 4 an = 5 · an-1 a) an = 4 · 5n b) an = 5 · 4n c) an = 4 · 5n-1 d) an = 5 · 4n-1

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Write the explicit formula for the geometric sequence represented by the recursive formula.
a1 = 4
an = 5 · an-1
a) an = 4 · 5n
b) an = 5 · 4n
c) an = 4 · 5n-1
d) an = 5 · 4n-1