# math Question

the 5th term in a geometric sequence is 160. The 7th term is 40. What are the possible values of the 6th term of the sequence

+70
70
+80
80

1. 👍 1
2. 👎 0
3. 👁 1,140
1. 40/160 = r^2, so r=±1/2

1. 👍 0
2. 👎 0
posted by Steve
2. a 5 = 160

a 6 = a 5 * q = 160 * q

a 7 = a 6 * q = a 5 * q * q = 160 * q ^ 2 = 40

160 q ^ 2 = 40 Divide both sides by 40

4 q ^ 2 = 1 Divide both sides by 4

q ^ 2 = 1 / 4 Take square root of both sides

q = + OR - 1 / 2

All number in progression is positive so q = 1 / 2

a 6 = a 5 * q = 160 * q

a 6 = 160 * 1 / 2 = 80

1. 👍 1
2. 👎 0
posted by Bosnian

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