The first three terms of a sequence are [tex]2x[/tex], [tex]y^2[/tex], and [tex]2xy^2[/tex]. The sequence continues by multiplying the previous two terms.

a) Select the 6th term of the sequence.

A. [tex]2x^2y^4[/tex]
B. [tex]2xy^4[/tex]
C. [tex]8x^3y^{10}[/tex]
D. [tex]6x^2y^8[/tex]



Answer :

To solve the problem, let's look at the given sequence and the rule for generating the subsequent terms.

The initial terms given are:
1. [tex]\(2x\)[/tex]
2. [tex]\(y^2\)[/tex]
3. [tex]\(2xy^2\)[/tex]

The rule for generating the sequence is to multiply the previous two terms to obtain the next term.

Let's calculate the next terms step by step.

Fourth Term:
To find the fourth term, we multiply the second term ([tex]\(y^2\)[/tex]) by the third term ([tex]\(2xy^2\)[/tex]):
[tex]\[ (y^2) \times (2xy^2) = 2xy^4 \][/tex]

Fifth Term:
To find the fifth term, we multiply the third term ([tex]\(2xy^2\)[/tex]) by the fourth term ([tex]\(2xy^4\)[/tex]):
[tex]\[ (2xy^2) \times (2xy^4) = 4x^2y^6 \][/tex]

Sixth Term:
To find the sixth term, we multiply the fourth term ([tex]\(2xy^4\)[/tex]) by the fifth term ([tex]\(4x^2y^6\)[/tex]):
[tex]\[ (2xy^4) \times (4x^2y^6) = 8x^3y^{10} \][/tex]

Therefore, the sixth term of the sequence is:
[tex]\[ 8x^3y^{10} \][/tex]

Finally, we can select the correct option:

[tex]\[ \boxed{C \ 8 x^3 y^{10}} \][/tex]