Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
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10-7<br />
Geometric Means A missing term or terms between two nonconsecutive terms in a<br />
geometric sequence are called geometric means. In the sequence 10, 20, 40, 80, …, the<br />
geometric mean between 10 <strong>and</strong> 40 is 20. You can use the formula a n a 1 r n 1 to find a<br />
geometric mean.<br />
Example<br />
Find the geometric mean in the sequence 6,<br />
In the sequence, a1 = 6 <strong>and</strong> a3 = 150. To find a2 , you must first find r.<br />
, 150.<br />
an a1 rn 1<br />
a3 a1 r3 1<br />
150 6 r<br />
Formula for the nth term of a geometric sequence<br />
n 3<br />
2<br />
<br />
a3 150 <strong>and</strong> a1 6<br />
Divide each side by 6.<br />
25 r2 6r<br />
Simplify.<br />
5 r Take the square root of each side.<br />
2<br />
150<br />
<br />
6 6<br />
If r 5, the geometric mean is 6(5) or 30. If r 5, the geometric mean is 6(5) or 30.<br />
Therefore the geometric mean is 30 or 30.<br />
Exercises<br />
NAME ______________________________________________ DATE ____________ PERIOD _____<br />
<strong>Study</strong> <strong>Guide</strong> <strong>and</strong> <strong>Intervention</strong> (<strong>continued</strong>)<br />
Geometric Sequences<br />
Find the geometric means in each sequence.<br />
1. 4, , 16 2. 12, , 108 3. 8, , 128<br />
4. 180, , 20 5. 2, , 98 6. 600, , 150<br />
1 1<br />
1 1<br />
3 15<br />
7. , , 8. , , 9. , , <br />
4 16<br />
2 32<br />
5 16<br />
2<br />
5<br />
2<br />
10. 14, , 11. , , 10 12. , , 54<br />
7<br />
8<br />
3<br />
13. 2.3, , 9.2 14. 137.7, , 15.3 15. 5.1, , 127.5<br />
3 3<br />
3<br />
16. , , 17. 15, , 18. 8, , 320,000<br />
8 32<br />
5<br />
© Glencoe/McGraw-Hill 616 Glencoe Algebra 1
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