Use the following to answer questions :
A geometric sequence has terms a₃ = 576 and a₆ = 243.
-Find the value of a₁.

Question

Use the following to answer questions : A geometric sequence has terms a 3 = 576 and a 6 = 243. -Find the value of a₁. A) 256 B) 1024 C) 3072 D) 4096

Quizplus · Accepted Answer

Using the formula for the nth term of a geometric sequence, we get:
aS1U1B13S1U1B0 = aS1U1B0(rS1U1B13S1U1B1)  and 
aS1U1B16S1U1B0 = aS1U1B0(rS1U1B16S1U1B1)
Taking their ratio, we have:
rS1U1B3S1U1B1 = (aS1U1B16S1U1B0 / aS1U1B13S1U1B0)^(1/3)
r = (243 / 576)^(1/3) = (3/4)^(1/3)
Using this value of r, we can find aS1U1B0 by plugging in the values of aS1U1B13S1U1B0, r, and n=13 into the formula:
aS1U1B13S1U1B0 = aS1U1B0(rS1U1B13S1U1B1)
576 = aS1U1B0((3/4)^(13))
aS1U1B0 = 1024
Finally, we can find aS1U1B11S1U1B0 by plugging in the values of aS1U1B0, r, and n=11 into the formula:
aS1U1B11S1U1B0 = aS1U1B0(rS1U1B11S1U1B1)
aS1U1B11S1U1B0 = 1024((3/4)^(11))
aS1U1B11S1U1B0 = 256

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