What is the recursive formula for this arithmetic sequence?โ7, โ1, 5, 11, ...A.{๐1=โ7๐๐=๐๐โ1โ6{ a 1โ =โ7a nโ =a nโ1โ โ6โ B.{๐1=11๐๐=๐๐โ1โ6{ a 1โ =11a nโ =a nโ1โ โ6โ C.{๐1=11๐๐=๐๐โ1+6{ a 1โ =11a nโ =a nโ1โ +6โ D.{๐1=โ7๐๐=๐๐โ1+6{ a 1โ =โ7a nโ =a nโ1โ +6โ SUBMITarrow_backPREVIOUS
Question
What is the recursive formula for this arithmetic sequence?โ7, โ1, 5, 11, ...A.{๐1=โ7๐๐=๐๐โ1โ6{ a 1โ =โ7a nโ =a nโ1โ โ6โ B.{๐1=11๐๐=๐๐โ1โ6{ a 1โ =11a nโ =a nโ1โ โ6โ C.{๐1=11๐๐=๐๐โ1+6{ a 1โ =11a nโ =a nโ1โ +6โ D.{๐1=โ7๐๐=๐๐โ1+6{ a 1โ =โ7a nโ =a nโ1โ +6โ SUBMITarrow_backPREVIOUS
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}.
Similar Questions
What is the recursive formula for this geometric sequence?โ4, โ24, โ144, โ864, ...A.{๐1=โ6๐๐=๐๐โ1โ4{ a 1โ =โ6a nโ =a nโ1โ โ4โ B.{๐1=โ4๐๐=๐๐โ1โ6{ a 1โ =โ4a nโ =a nโ1โ โ6โ C.{๐1=โ4๐๐=๐๐โ1โ30{ a 1โ =โ4a nโ =a nโ1โ โ30โ D.{๐1=โ6๐๐=๐๐โ1โ30{ a 1โ =โ6a nโ =a nโ1โ โ30โ
Which recursive formula can be used to represent the sequence 2, 4, 6, 8, 10, ... ?A.๐1=0๐๐=๐๐โ1+2โ a 1โ =0a nโ =a nโ1โ +2โ B.๐1=2๐๐=๐๐โ1โ2โ a 1โ =2a nโ =a nโ1โ โ2โ C.๐1=2๐๐=๐๐โ1+2โ a 1โ =2a nโ =a nโ1โ +2โ D.๐1=2๐๐=๐๐โ1โ2โ a 1โ =2a nโ =a nโ1โ โ2โ SUBMITarrow_backPREVIOUS
What is the explicit formula for this arithmetic sequence?โ11, โ18, โ25, โ32, ...A.an = โ11 + (n โ 1)7B.an = โ11 + (n โ 1)(โ7)C.an = โ7 + (n โ 1)(โ11)D.an = 11 + (n โ 1)(โ7)
Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 2 + (n โ 1)5?A.{๐1=5๐๐=(๐๐โ1+5)2{ a 1โ =5a nโ =(a nโ1โ +5)2โ B.{๐1=2๐๐=๐๐โ1โ5{ a 1โ =2a nโ =a nโ1โ โ5โ C.{๐1=5๐๐=๐๐โ1+2{ a 1โ =5a nโ =a nโ1โ +2โ D.{๐1=2๐๐=๐๐โ1+5{ a 1โ =2a nโ =a nโ1โ +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 = anโ1 + ________What number belongs in the blank space in the recursive formula?A.19B.5C.13D.6SUBMITarrow_backPREVIOUS
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.