Knowee
Questions
Features
Study Tools

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

Question

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

๐Ÿง Not the exact question you are looking for?Go ask a question

Solution

The recursive formula for an arithmetic sequence is given by a_n = a_(n-1) + d, where d is the common difference.

In this sequence, the common difference (d) can be found by subtracting the first term from the second term, or the second term from the third term, and so on.

So, d = -1 - (-7) = 6 or d = 5 - (-1) = 6.

The first term (a_1) of the sequence is -7.

Therefore, the recursive formula for this sequence is a_n = a_(n-1) + 6 with a_1 = -7.

So, the correct answer is D. {a_1 = -7, a_n = a_(n-1) + 6}.

This problem has been solved

Similar Questions

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€‹

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

What is the explicit formula for this arithmetic sequence?โ€“11, โ€“18, โ€“25, โ€“32, ...A.an = โ€“11 + (n โ€“ 1)7B.an = โ€“11 + (n โ€“ 1)(โ€“7)C.an = โ€“7 + (n โ€“ 1)(โ€“11)D.an = 11 + (n โ€“ 1)(โ€“7)

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€‹

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

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.