Question

given: $a_n = -3n + 9$ find term number 43 in the arithmetic sequence

Explanation:

Step1: Identify the formula for the nth term

The formula for the nth term of the arithmetic sequence is given as \( a_n = -3n + 9 \). To find the 43rd term, we need to substitute \( n = 43 \) into this formula.

Step2: Substitute n = 43 into the formula

Substitute \( n = 43 \) into \( a_n = -3n + 9 \):
\[
a_{43} = -3(43) + 9
\]

Step3: Calculate the value

First, calculate \( -3 \times 43 \):
\[
-3 \times 43 = -129
\]
Then, add 9 to the result:
\[
a_{43} = -129 + 9 = -120
\]

Answer:

\( -120 \)