Question

Using two or more complete sentences, describe how to find the general rule for the geometric sequence with a4=3 and a6=3/16. In your final answer, include all of your calculations.

Answer 1

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.

What is geometric sequence?

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 r 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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