Question

Use inductive reasoning to describe the pattern of the sequence. Then find the next two terms. 6, 24, 96, 384, ...

A. Multiply by 3; 672, 960.

B. Multiply by 4.5; 402, 420.

C. Multiply by 4; 1536, 6144.

D. Multiply by 3.5, 576, 764.​

Answer 1

Answer:

1536 and 6144

Step-by-step explanation:

you are multiplying by 4

I hope this helps you to understands better

Answer 2

The next two-term of the sequence is 1536 and 6144 and the multiplicity is 4

Given the sequence of numbers expressed as 6, 24, 96, 384, ...

The given sequence is a geometric sequence. The nth term of the sequence is expressed as;

$T_n = ar^{n-1}$

a is the first term

r is the common ratio or multiplicity

n is the number of terms

Given the following parameters

a = 6

r = 24/6 = 96/24 = 4

n = 5 and 6 (5th and 6th term)

For the fifth term;

$T_{5} = 6(4)^{5-1}\\T_5=6(4)^4\\T_5 = 1536$

For the sixth term;

$T_{6} = 6(4)^{6-1}\\T_6=6(4)^5\\T_6 = 6144$

Hence the next two-term of the sequence is 1536 and 6144 and the multiplicity is 4

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