Question

check your understanding
the first two terms of an arithmetic sequence, a(n), are shown.
-5, -2, …
what is the value of a(6)?
a(6) = \square

Explanation:

Step1: Find the common difference \( d \)

The common difference \( d \) in an arithmetic sequence is the difference between consecutive terms. So, \( d = a(2) - a(1) \). Given \( a(1) = -5 \) and \( a(2) = -2 \), we have \( d = -2 - (-5) = -2 + 5 = 3 \).

Step2: Use the arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( a(n) = a(1) + (n - 1)d \). We need to find \( a(6) \), so substitute \( a(1) = -5 \), \( d = 3 \), and \( n = 6 \) into the formula.
First, calculate \( (n - 1)d \): \( (6 - 1) \times 3 = 5 \times 3 = 15 \).
Then, find \( a(6) \): \( a(6) = a(1) + 15 = -5 + 15 = 10 \).

Answer:

10