Answer: The first four terms of the given geometric sequence are 3, -9, 27 and -81.
Step-by-step explanation: We are given to find the first four terms of the geometric sequence, where
first term is 3 and common ratio is -3.
That is
\(a=3,~~~r=-3.\)
We know that
the n-th term of a geometric series with first term a and common ratio r is given by
\(a_n=ar^{n-1}.\)
Therefore, the first four terms are
\(a_1=ar^{1-1}=3\times (-3)^0=3,\\\\a_2=ar^{2-1}=3\times (-3)^{1}=-9,\\\\a_3=ar^{3-1}=3\times (-3)^2=27,\\\\a_4=ar^{4-1}=3\times (-3)^3=-81.\)
Thus, the first four terms of the given geometric sequence are 3, -9, 27 and -81.
