Question

Arithmetic progressions. p+3, 3p+4, 5p+5,......,23p+14

Answer 1

Answer:  $\bold{a_1=p+3,\quad d=2p+1,\quad a_n=(2p+1)\cdot a_{n-1}}$

Step-by-step explanation:

p + 3, 3p + 4, 5p + 5, ... , 23p + 14

Notice that each p-term is increased by 2p.

Notice that each number is increased by 1

So, the difference (d) is: 2p + 1

$\text{The general form for the recursive rule of an arithmetic sequence is:}\\a_n=d\cdot a_{n-1}\quad \text{where d is the difference and}\ a_{n-1}\ \text{is the previous term}$

$\text{So, the recursive rule with the information provided is:}\\a_n=(2p+1)\cdot a_{n-1}$