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)}`

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)`