Question

Which of the following define the same Arithmetic Sequence using a Recursive Formula

Answer 1

The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is $a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)$

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,

$a_n=a_1+(n-1)d$

By Recursive Formula,

$a_n=a_{n - 1}+d$

In the first choice: a₁ = -23 and

$a_n=a_{n-1}+12$

Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.

and

$a_n=-23+12(n-1)$

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

$a_n=a_{n-1}+1$

By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.

$a_n=100-1(n-1)$

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

$a_n=a_{n-1}+12$

By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.

$a_n=12-41(n-1)$

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

$a_n=a_{n-1}-4$

By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.

$a_n=50+4(n-1)$

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 -

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