Question

how many terms are in the arithmetic sequence 9, 2, -5, ..., -187? hint: $a(n) = a(1) + d(n - 1)$, where $a(1)$ is the first term and $d$ is the common difference. \bigcirc 27 \bigcirc 28 \bigcirc 30 \bigcirc 29

Explanation:

Step1: Identify first term and common difference

First term \( A(1) = 9 \). Common difference \( d = 2 - 9 = -7 \).

Step2: Use arithmetic sequence formula

The formula is \( A(n) = A(1) + d(n - 1) \). We know \( A(n) = -187 \), so substitute values:
\( -187 = 9 + (-7)(n - 1) \)

Step3: Solve for \( n \)

First, simplify the equation:
\( -187 - 9 = -7(n - 1) \)
\( -196 = -7(n - 1) \)
Divide both sides by -7:
\( 28 = n - 1 \)
Add 1 to both sides:
\( n = 29 \)

Answer:

29