The steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

<h3>What is geometric sequence?</h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

$a_n=a_1r^{n-1}$

Here, a₁ is the first term of the sequence and <em>r </em>is the common ratio.

The fourth term and sixth term given in for the geometric sequence are 3 and 3/16. For the fourth term,

$a_4=a_1r^{4-1}\\3=a_1r^3$ ...1

For the sixth term,

$a_6=a_1r^{6-1}\\\dfrac{3}{16}=a_1r^5$ ....2

On solving, we get, a₁=192 and r=1/4. Thus, the geometric sequence can be given as,

$a_n=a_1r^{n-1}\\a_n=192\times\dfrac{1}{4}^{n-1}$

Hence, the steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

Learn more about the geometric sequence here;

brainly.com/question/1509142

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3 years ago