Question

An arithmetic sequence has a common difference of 2 and contains the value 86 at some point in the sequence. Which of the following recursive formulas could represent this sequence?
Group of answer choices

an = an – 1 + 2; a1 = 1

an = an – 1 + 2; a1 = 2

an = an – 1 + 1; a1 = 2

an = an – 1 + 1; a1 = 1

Answer 1

Answer:

B. $a_{n} = a_{n-1}+2$; $a_{1} = 2$

Step-by-step explanation:

According to the statement, we find that the following two conditions must be observed:

$a_{i} = 86$ (Eq. 1)

$a_{i}-a_{i-1} = 2$ (Eq. 2)

Since the difference between two even numbers leads to another even number. Hence, $a_{1}$ must be an even number and the correct answer is B.