Question

What is the recursive formula for the explicit formula an = 30 + 14n, and what is the first term of the sequence?

Options:
A) an = an-1 + 14, a1 = 44
B) an = an-1 + 30, a1 = 30
C) an = an-1 + 14, a1 = 30
D) an = an-1 + 30, a1 = 44

Answer 1

The recursive formula for the explicit formula a_n = 30 + 14n is a_n = a_n-1 + 14 with the first term being a_1 = 44, making option A correct.

Step-by-step explanation:

To find the recursive formula for the explicit formula an = 30 + 14n, we need to express the nth term as a function of the (n-1)th term. To do this, let's first calculate the first term of the sequence (a1) by substituting n=1 into the explicit formula:

a1 = 30 + 14(1) = 30 + 14 = 44.

Now, let's calculate the second term (a2):

a2 = 30 + 14(2) = 30 + 28 = 58.

Observing the difference between successive terms, we see that each term is 14 more than the previous one. Thus, the recursive formula would be:

an = an-1 + 14, where the first term is a1 = 44. Therefore, the right option is A) an = an-1 + 14, a1 = 44.