ACTIVITY: 1. In the geometric sequence -2,6,-18, 54, ..., what is the 7th term? 2. How many terms are there in the geometric sequence whose first term is 50, last term is 25, and common ratio is - 1 3. A cellphone costs 10 000 in 2015. If it depreciates its value by 2% each year, how much will it be in 2020?
Answer (1)
Answer:1. r = a2/a1r = 6/-2r = -3----------------an = a1 * r^(n-1)a7 = (-2) * (-3)^(7-1)a7 = (-2) * (-3)^(6)a7 = (-2) * 729a7 = -14582. Zero. It's not possible.an = a1 * r^(n-1)25 = 50 * (-1)^(n-1)25/50 = 50/50 * (-1)^(n-1)1/2 = (-1)^(n-1)---> -1 to the raised to the power of any number is always either -1 or 1, which isn't equal to 1/2 and doesn't satisfy both sides of the equation.3. V = P * (1-r)^tA = 10000 * (1-0.02)^5A = 10000 * (0.98)^5A = 10000 * 0.9039207A = 9039.21
