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