What is s8 in the sequence 1/2,-1/6,1/18?

To find the general term s8 in the sequence 1/2, -1/6, 1/18, we need to determine the pattern or rule that governs this sequence. Let's analyze the given terms: 1/2, -1/6, 1/18 The sequence appears to alternate between positive and negative terms and the denominators are powers of 3 (2^1, 2^2, 2^3). It seems like the pattern is that each term is (1/3) times the previous term, with alternating signs. So, we can express the general term s(n) as: s(n) = (-1)^(n+1) * (1/2) * (1/3)^(n-1) Now, let's find s8: s(8) = (-1)^(8+1) * (1/2) * (1/3)^(8-1) s(8) = (-1)^9 * (1/2) * (1/3)^7 s(8) = -1 * (1/2) * (1/3)^7 Now, calculate the value: s(8) = -1 * (1/2) * (1/2187) s(8) = -1/4374 So, s8 in the sequence is -1/4374.