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Which of the following recursive formulas represents the same geometric sequence as the formula an = 2 โ€ข 3(n โ€“ 1)?A.{๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™2{ a 1โ€‹ =3a nโ€‹ =a nโˆ’1โ€‹ โˆ™2โ€‹ B.{๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2{ a 1โ€‹ =3a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ C.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™3{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™3โ€‹ D.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™6{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™6โ€‹ SUBMITarrow_backPREVIOUS

Question

Which of the following recursive formulas represents the same geometric sequence as the formula an = 2 โ€ข 3(n โ€“ 1)?A.{๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™2{ a 1โ€‹ =3a nโ€‹ =a nโˆ’1โ€‹ โˆ™2โ€‹ B.{๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2{ a 1โ€‹ =3a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ C.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™3{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™3โ€‹ D.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™6{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™6โ€‹ SUBMITarrow_backPREVIOUS

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Solution

The given formula is an = 2 โ€ข 3(n โ€“ 1). This is a geometric sequence where the common ratio is 3 and the first term is 2.

Let's analyze the options:

A. {๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™2: This option has the first term as 3 and the common ratio as 2. This does not match the given formula.

B. {๐‘Ž1=3๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2: This option is not a geometric sequence because the nth term is not a multiple of the previous term.

C. {๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™3: This option has the first term as 2 and the common ratio as 3. This matches the given formula.

D. {๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™6: This option has the first term as 2 but the common ratio is 6. This does not match the given formula.

So, the correct answer is C. {๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™3.

This problem has been solved

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