Find the exact value of the eighth term of the geometric sequence: 648,216,72,24

8th term is 0.30

Step-by-step explanation:

⇒ r = a2/a1 = 216/648 = 1/3

⇒ 8th term =  648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30

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step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: