Answer:
63
Step-by-step explanation:
Each term in a geometric sequence progresses by multiplying a constant (let us name it r).
Let us solve for this constant r in order to find the 13th term.
If the seventh term is 7, the tenth term would be 7*r*r*r, or [tex]7r^{3}[/tex]. We also happen to know that the 10th term is 21. Let us make a new equation:
[tex]7r^{3} =21\\r^{3}=3\\r= \sqrt[3]{3}[/tex]
or, approx. 1.442249570307408
Using the same logic, the 13th term would be 7*r*r*r*r*r*r, or [tex]7r^{6}[/tex]. We may now substitute what we know, r, into this expression to obtain the 13th term:
[tex]7*\sqrt[3]{3}^{6} = \\7*3^{2}=\\7*9=\\63[/tex]
Therefore, the 13th term of this progression is 63.
I hope this helps! Please let me know if you have any further questions :)
