Questions: Write the first five terms of the geometric sequence. an=-8 an-1 ; a1=-4 -8,-32,-256,-2048,-16,384 -4,-12,-20,-28,-36 32,-256,2048,-16,384,131,072 -4,32,-256,2048,-16,384

Solution Steps

To find the first five terms of the geometric sequence given by \( a_{n} = -8 a_{n-1} \) and \( a_{1} = -4 \), we start with the initial term \( a_{1} \) and repeatedly multiply by the common ratio, which is -8, to find the subsequent terms.

The first term of the geometric sequence is given as \( a_1 = -4 \).

Using the recursive formula \( a_n = -8 a_{n-1} \), we calculate the next four terms:

• \( a_2 = -8 \cdot a_1 = -8 \cdot (-4) = 32 \)
• \( a_3 = -8 \cdot a_2 = -8 \cdot 32 = -256 \)
• \( a_4 = -8 \cdot a_3 = -8 \cdot (-256) = 2048 \)
• \( a_5 = -8 \cdot a_4 = -8 \cdot 2048 = -16384 \)

The first five terms of the geometric sequence are: \[ a_1 = -4, \quad a_2 = 32, \quad a_3 = -256, \quad a_4 = 2048, \quad a_5 = -16384 \]

Final Answer