Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\th}$ term.
$\left\lbrace-9,-4,1,6,\ldots\right\rbrace$

• A. 46
• B. 136
• C. 146
• D. 150

Answer: (B)

Verified step by step guidance

1. Identify the first term of the sequence, which is \( a_1 = -9 \).
2. Determine the common difference \( d \) by subtracting the first term from the second term: \( d = -4 - (-9) = 5 \).
3. Use the formula for the nth term of an arithmetic sequence: \( a_n = a_1 + (n-1) imes d \).
4. Substitute the known values into the formula to find the 30th term: \( a_{30} = -9 + (30-1) imes 5 \).
5. Simplify the expression to find the value of the 30th term.