Question

CALC Which choices describe a Subscript n Baseline = 4 (0.9) Superscript n? Check all that apply.

S1 = 4
S2 = 6.84
S3 = 10.156

The sequence diverges.

Answer 1

Answer:

B and D

Step-by-step explanation:

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Answer 2

$S_{2}=6.84$

$S_{\infty} = \frac{3.6}{1-0.9}$.

These two describes $a_{n}= 4(0.9)^{n}$

Option B and D are correct.

What is geometrical sequence?

A geometric sequence is a sequence of numbers where each term after the first term is found by multiplying the previous one by a fixed non-zero number, called the common ratio.

In a geometric sequence, every term is multiplied by a constant which results in its next term. So a geometric sequence is in form a, ar, a$r^{2}$... where 'a' is the first term and 'r' is the common ratio of the sequence. The common ratio can be either a positive or a negative number.

Given

$a_{n}= 4(0.9)^{n}$

This is a geometrical sequence

q = 0.9 is the common ratio

$a_{1} =4(0.9)^{1}$ = 3.6

$S_{n} = \frac{a_{1} \times (1 - q^{n}) }{1-q} = \frac{a_{n} q-a_{1} }{q-1}$

= $\frac{3.6(0.9)^{n}-3.6 }{0.9-1}$ = $10[3.6-3.6(0.9)^{n} ]$

$S_{1} = 10[3.6 -3.6 \times 0.9] = 3.6$

$S_{2} = 10[3.6 -3.6 \times 0.9^{2} ] = 6.84$

$S_{2} = 10[3.6 -3.6 \times 0.9^{3} ] = 9.756$

$S_{\infty} = \frac{3.6}{1-0.9}$

$S_{n} = \frac{a_{1} \times (1 - q^{n}) }{1-q} \\ \lim_{n \to \infty} 1-q^{n} = 1$

∴ $S_{\infty} = \frac{q_{1} }{1-q}$

Hence,

$S_{2}=6.84$

$S_{\infty} = \frac{3.6}{1-0.9}$.

These two describes $a_{n}= 4(0.9)^{n}$.

Option B and D are correct.

Find out more information about geometrical sequence here

brainly.com/question/11266123

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