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

B.
`a_(n) = a_(n-1)+2`;
`a_(1) = 2`

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.