find the sum of the 7 terms of -6, -18, -54,...
Answer (1)
Answer:Step-by-step explanation:The sum of the first 7 terms of the geometric sequence -6, -18, -54, ... is -2184. ExplanationIdentify the sequence type: The given sequence is a geometric progression (GP) because each term is multiplied by the same number (3) to get the next term. Identify the first term and common ratio: The first term (a) is -6, and the common ratio (r) is -18/-6 = 3. Use the formula for the sum of a GP: The sum (Sn) of the first n terms of a GP is given by: Sn = a(1 - r^n) / (1 - r) Substitute the values: In this case, a = -6, r = 3, and n = 7. So, S7 = -6 * (1 - 3^7) / (1 - 3) Calculate: S7 = -6 * (1 - 2187) / (-2) = -6 * (-2186) / (-2) = -6 * 1093 = -2184.
