Questions: Unit Review - Introduction to ... Find the 24th term of this arithmetic sequence. -21,-14,-7,0,7, ... a24=[?] Hint: an=a1+(n-1) d

Transcript text: Unit Review - Introduction to ... Find the 24th term of this arithmetic sequence. \[ \begin{array}{c} -21,-14,-7,0,7, \ldots \\ a_{24}=[?] \end{array} \] Hint: $a_{n}=a_{1}+(n-1) d$

Solution

Solution Steps

Step 1: Identify the first term and common difference

The given arithmetic sequence is: \[ -21, -14, -7, 0, 7, \ldots \] The first term $a_1$ is $-21$. To find the common difference $d$, subtract the first term from the second term: \[ d = -14 - (-21) = 7 \]

Step 2: Use the formula for the $n$-th term of an arithmetic sequence

The formula for the $n$-th term of an arithmetic sequence is: \[ a_n = a_1 + (n-1)d \] We are asked to find the 24th term ($a_{24}$).

Step 3: Substitute the known values into the formula

Substitute $a_1 = -21$, $d = 7$, and $n = 24$ into the formula: \[ a_{24} = -21 + (24-1) \cdot 7 \] \[ a_{24} = -21 + 23 \cdot 7 \] \[ a_{24} = -21 + 161 \] \[ a_{24} = 140 \]

Final Answer

\[ \boxed{a_{24} = 140} \]

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