In this item, we are to calculated for the 6th term of the geometric sequence given the initial value and the common ratio. This can be calculated through the equation,
An = (A₀)(r)ⁿ ⁻ ¹ where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms.
Substitute the known values to the equation,
An = (5)(-1/2)⁶ ⁻ ¹ An = -5/32
Hence, the answer to this item is the third choice, -5/32.
To cube something means to take it by 3, when used in the sentance, 3 cubed it refers to 3^3 power which means 3*3*3 which equals 21. In this context I'm guessing that they mean 50^3 which would be $125,000.
