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
4 answers
40/160 = r^2, so r=±1/2
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
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
What is the answer???
80 or +-80??
80 or +-80??
80