Questions: Find the first four terms of the sequence given by the following. [ an=6 cdot(-3)^n-1, quad n=1,2,3 ldots ]

Solution Steps

The sequence is given by the formula: \[ a_{n} = 6 \cdot (-3)^{n-1} \] where \( n \) is a positive integer starting from 1. We need to find the first four terms of this sequence.

For \( n = 1 \): \[ a_{1} = 6 \cdot (-3)^{1-1} = 6 \cdot (-3)^{0} = 6 \cdot 1 = 6 \]

For \( n = 2 \): \[ a_{2} = 6 \cdot (-3)^{2-1} = 6 \cdot (-3)^{1} = 6 \cdot (-3) = -18 \]

For \( n = 3 \): \[ a_{3} = 6 \cdot (-3)^{3-1} = 6 \cdot (-3)^{2} = 6 \cdot 9 = 54 \]

For \( n = 4 \): \[ a_{4} = 6 \cdot (-3)^{4-1} = 6 \cdot (-3)^{3} = 6 \cdot (-27) = -162 \]

Final Answer