Question

a certain arithmetic sequence has the following explicit formula for the nth term: an = 2 + (n - 1)(6) The same sequence has the following recursive formula: an = an - 1 + ___ what number belongs in the blank space in the recursive formula? A. 6 B. 2 C. 12 D. 4

Answer 1

Answer:

A. 6

Step-by-step explanation:

The formula for nth arithmetic sequence =

aₙ = a₁+(n - 1) d

a₁ = First term

n = number of terms

d = common difference

In the question above, explicit formula for the nth term:

aₙ = 2 + (n - 1)(6)

This means, the first term a1 = 2

d = 6

The same sequence has the following recursive formula:

aₙ = aₙ₋₁+ ___

The formula for a recursive formula is

aₙ= aₙ₋₁+ d

Where the common difference from the nth term = 6

Therefore , the number that belongs in the blank space in the recursive formula is 6