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
Question
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
Solution
The explicit formula given is an = 2 + (n โ 1)5. This represents an arithmetic sequence where the first term (a1) is 2 and the common difference (d) is 5.
Looking at the options:
A. {๐1=5๐๐=(๐๐โ1+5)2: This is incorrect because the first term is not 2 and the common difference is not 5.
B. {๐1=2๐๐=๐๐โ1โ5: This is incorrect because the common difference is not multiplication, it should be addition.
C. {๐1=5๐๐=๐๐โ1+2: This is incorrect because the first term is not 2 and the common difference is not 5.
D. {๐1=2๐๐=๐๐โ1+5: This is correct because the first term is 2 and the common difference is 5.
So, the answer is D. {๐1=2๐๐=๐๐โ1+5.
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