Question

HOW CAN ARITHMETIC AND GEOMETRIC SEQUENCES BECOME LINEAR AND EXPONENTIAL FUNCTIONS?

Answer 1

The formula of an arithmetic sequence is the following :
$u_n=r\times n+u_0\text{ wherein r is the rate of the sequence} \\\text{and u0 the first value}\\\text{The above formula is linear wherever }u_0=0.$
A geometric sequence is in the form:
$u_n=u_0r^n\text{, again u0 the first value and r the rate. }\\\text{If }u_0=1\text{ the formula becomes:}\\u_n=r^n=e^{n\log r}\text{ which is an exponential formula.}$