1) Explain why arithmetic sequences best modelled with linear functions?2)Explain why geometric sequences best modelled with exponential function?

Accepted Solution

Answer:1.) Arithmetic sequences are modeled with linear functions because it is a linear series2.) Geometric sequences are modeled with exponential functions because their value increases exponentiallyStep-by-step explanation:1.) Arithmetic sequences are linear functions. While the n-value increases by a constant value of one, the f (n) value increases by a constant value of d, the common difference. Arithmetic Sequence is one where you add (or subtract) the same value to get from one term to the next.2.) An exponential function is obtained from a geometric sequence by replacing the counting integer n by the real variable x. Geometric sequences (with common ratio not equal to βˆ’1, 1 or 0) show exponential growth or exponential decay, as opposed to the linear growth (or decline) of an arithmetic progression such as 4, 15, 26, 37, 48, … (with common difference 11).This shows that Geometric series grow or decays (reduces) exponentially; this is due to their common ratio (r)