Question

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Answer 1

The first 4 terms in the sequence are...

A) {4, .8, .16, .032,...}.

Further explanation

Geometry sequence are series of numbers that have a constant ratio

or can be interpreted:

Each number is obtained by multiplying the previous number by a constant

The sequence can be:

a, ar, ar², ar³, ... etc.

Can be formulated

$\large{\boxed{\bold x_n=ar^{n-1}}}$

where:

a is the first term, and

r is the common ratio

In an geometric sequence , if a1 = 4 and r = 0.2, the first 4 terms in the sequence are

• n=1

$\displaystyle x_1=4=a$

• n=2

$\displaystyle x_2=4\times 0.2^{2-1}\\\\x_2=4\times 0.2^{1}\\\\x_2=4\times 0.2\\\\x_2=0.8$

• n=3

$\displaystyle x_3=4\times 0.2^{3-1}\\\\x_2=4\times 0.2^{2}\\\\x_2=4\times 0.04\\\\x_2=0.16$

• n=4

$\displaystyle x_4=4\times 0.2^{4-1}\\\\x_2=4\times 0.2^{3}\\\\x_2=4\times 0.008\\\\x_2=0.032$

Learn more

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Keywords : a geometric sequence, the first term, the common ratio

Answer 2

A.) {4,.8,.16,.032,...}


Begin with 4 and multiply by 0.2, the ratio, to obtain successive term.