The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is
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,
By Recursive Formula,
In the first choice: a₁ = -23 and
Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.
and
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
By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.
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
By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.
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
By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.
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.
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