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Which recursive formula can be used to represent the sequence 2, 4, 6, 8, 10, ... ?A.๐‘Ž1=0๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2โ€‹ a 1โ€‹ =0a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ B.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™2โ€‹ C.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ D.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ’2โ€‹ SUBMITarrow_backPREVIOUS

Question

Which recursive formula can be used to represent the sequence 2, 4, 6, 8, 10, ... ?A.๐‘Ž1=0๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2โ€‹ a 1โ€‹ =0a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ B.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™2โ€‹ C.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ D.๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’2โ€‹ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ’2โ€‹ SUBMITarrow_backPREVIOUS

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Solution

The correct answer is C. ๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2โ€‹. This is because the sequence starts with 2 (๐‘Ž1=2) and each subsequent term is 2 more than the previous term (๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2).

Similar Questions

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

What is the recursive formula for this arithmetic sequence?โ€“7, โ€“1, 5, 11, ...A.{๐‘Ž1=โˆ’7๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’6{ a 1โ€‹ =โˆ’7a nโ€‹ =a nโˆ’1โ€‹ โˆ’6โ€‹ B.{๐‘Ž1=11๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’6{ a 1โ€‹ =11a nโ€‹ =a nโˆ’1โ€‹ โˆ’6โ€‹ C.{๐‘Ž1=11๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+6{ a 1โ€‹ =11a nโ€‹ =a nโˆ’1โ€‹ +6โ€‹ D.{๐‘Ž1=โˆ’7๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+6{ a 1โ€‹ =โˆ’7a nโ€‹ =a nโˆ’1โ€‹ +6โ€‹ SUBMITarrow_backPREVIOUS

Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 2 + (n โ€“ 1)5?A.{๐‘Ž1=5๐‘Ž๐‘›=(๐‘Ž๐‘›โˆ’1+5)2{ a 1โ€‹ =5a nโ€‹ =(a nโˆ’1โ€‹ +5)2โ€‹ B.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™5{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ โˆ™5โ€‹ C.{๐‘Ž1=5๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+2{ a 1โ€‹ =5a nโ€‹ =a nโˆ’1โ€‹ +2โ€‹ D.{๐‘Ž1=2๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+5{ a 1โ€‹ =2a nโ€‹ =a nโˆ’1โ€‹ +5โ€‹

What is the recursive formula for this geometric sequence?โ€“4, โ€“24, โ€“144, โ€“864, ...A.{๐‘Ž1=โˆ’6๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™4{ a 1โ€‹ =โˆ’6a nโ€‹ =a nโˆ’1โ€‹ โˆ™4โ€‹ B.{๐‘Ž1=โˆ’4๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™6{ a 1โ€‹ =โˆ’4a nโ€‹ =a nโˆ’1โ€‹ โˆ™6โ€‹ C.{๐‘Ž1=โˆ’4๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™30{ a 1โ€‹ =โˆ’4a nโ€‹ =a nโˆ’1โ€‹ โˆ™30โ€‹ D.{๐‘Ž1=โˆ’6๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ™30{ a 1โ€‹ =โˆ’6a nโ€‹ =a nโˆ’1โ€‹ โˆ™30โ€‹

A certain arithmetic sequence has this explicit formula for the nth term:an = 13 + (n โ€“ 1)(6)The same sequence has this recursive formula:an = anโ€“1 + ________What number belongs in the blank space in the recursive formula?A.19B.5C.13D.6SUBMITarrow_backPREVIOUS

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