Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is [tex]a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)[/tex]
If first term of a arithmatic sequence is a₁ and the common difference is d then,
By Explicit Formula, the n-th term of the sequence is given by,
[tex]a_n=a_1+(n-1)d[/tex]
By Recursive Formula,
[tex]a_n=a_{n - 1}+d[/tex]
In the first choice: a₁ = -23 and
[tex]a_n=a_{n-1}+12[/tex]
Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.
and
[tex]a_n=-23+12(n-1)[/tex]
So by explicit formula it also suggests arithmatic sequence with first term -23 and common difference 12.
So it is one correct choice.
In second choice: a₁ = -100 and
[tex]a_n=a_{n-1}+1[/tex]
By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.
[tex]a_n=100-1(n-1)[/tex]
By explicit formula, it suggests arithmatic sequence with first term 100 and common difference -1.
So it is not the correct choice.
In third choice: a₁ = -41 and
[tex]a_n=a_{n-1}+12[/tex]
By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.
[tex]a_n=12-41(n-1)[/tex]
By explicit formula, it suggests arithmatic sequence with first term 12 and common difference -41.
So it is not the correct choice.
In fourth choice: a₁ = 50 and
[tex]a_n=a_{n-1}-4[/tex]
By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.
[tex]a_n=50+4(n-1)[/tex]
By explicit formula, it suggests arithmatic sequence with first term 50 and common difference 4.
So it is not the correct choice.
Hence the option (A), the first choice is correct.
Learn more about Arithmatic Sequence here -
https://brainly.com/question/6561461
#SPJ10
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.