Questions: Find the 29th term. 20, 14, 8, 2, -4, ... 29th term = [?] 1st term + common difference(desired term -1)

Transcript text: Find the 29th term. \[ \begin{array}{c} 20,14,8,2,-4, \ldots \\ 29^{\text {th }} \text { term }=[?] \end{array} \] 1st term + common difference(desired term -1 )

Solution

Solution Steps

Step 1: Identify the Sequence

The given arithmetic sequence is \( 20, 14, 8, 2, -4, \ldots \). The first term \( a_1 \) is \( 20 \) and the common difference \( d \) can be calculated as: \[ d = 14 - 20 = -6 \]

Step 2: Apply the Formula for the nth Term

To find the 29th term \( a_{29} \) of the sequence, we use the formula for the nth term of an arithmetic sequence: \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values: \[ a_{29} = 20 + (29 - 1) \cdot (-6) \]

Step 3: Calculate the 29th Term

Now, we simplify the expression: \[ a_{29} = 20 + 28 \cdot (-6) = 20 - 168 = -148 \]