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Kristin Fracchia

ACT Challenge Question 14: Geometric Series – Explanation

Magoosh ACT Challenge Question


Earlier this week, we posted a challenging ACT Math problem on geometric sequences. Here it is again if you missed it. Give it a try, then scroll below for the explanation!

ACT Challenge Question 14

In a geometric sequence in which all of the terms are positive, the second term is 2 and the fourth term is 10. What is the value of the seventh term in the sequence?


Answer and Explanation:

D. act1ge_img2

In a geometric series, each term is the product of previous term times some common ratio.  We multiply by the common ratio to change any one term into its successor.

Here, we don’t know the common ratio, so let it be r.


But we know the numerical value of the fourth term.


Because every term is positive, we don’t have to consider the negative square root.  Now that we have the common ratio, we can move from term to term.  Each time, we multiply by the square root of 5.


So our answer is D.


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About Kristin Fracchia

Kristin makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of train running, backpacking, hot yoga, and esoteric knowledge.

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