Question

Find a formula a(n) for the nth term of the arithmetic sequence whose first term is a(1) = −3 such that an 1 − a(n) = 4 for n≥1.

a) a(n) = −3+4(n−1)
b) a(n) = −3+4n
c) a(n) = −3 + (4 / n-1)​
d) a(n) = −3 + (4 / n)​

Answer 1

The nth term of the arithmetic sequence is correctly given by formula a(n) = −3 + 4(n−1), which accounts for a first term of −3 and a common difference of 4.

Step-by-step explanation:

The student has asked to find a formula for the nth term of an arithmetic sequence where the first term is a(1) = −3 and the common difference is given by a(n + 1) − a(n) = 4. It's clear that the correct formula for the nth term of this sequence would be a(n) = a(1) + (n-1)d, where d is the common difference, which in this case is 4. Substituting the given values into the formula gives us a(n) = −3 + (n-1)×4.

Answer choice (a), a(n) = −3+4(n−1), correctly represents this arithmetic sequence as it starts with the first term −3 and adds the common difference of 4, multiplied by one less than the term number (because the common difference is applied starting with the second term).