Question

The recursive formula for a sequence is Un =U n-1 +12 , where Un is the nth term of the sequence and U₁ =19 Which explicit formula can be used to determine the nth term of the sequence?

Answer 1

The explicit formula for the nth term of the arithmetic sequence defined by Un = Un-1 + 12 and U1 = 19 is Un = 12n + 7.

Step-by-step explanation:

The recursive formula given is Un = Un-1 + 12, where U1 = 19 represents the first term of the sequence. This is an arithmetic sequence since the difference between consecutive terms is constant. To find the explicit formula for the nth term, we use the arithmetic sequence formula:

Un = U1 + (n - 1)d,

where U1 is the first term and d is the common difference between the terms. Substituting the given values into the formula:

Un = 19 + (n - 1) × 12,

Expanding and simplifying, we get:

Un = 12n + 7.

Therefore, to find the nth term of the sequence, we can use the explicit formula Un = 12n + 7.