Question

Write a rule for nth term of an arithmetic sequence with a(low 8) and d=5

Answer 1

First, generate the first few terms of the sequence.
\[a _{1}=8\]
\[a _{2}=8+5=13\]
But write down HOW you got \[a _{2}\]
\[a _{2}=8+5=a _{1}+5\]
Continue this for the next terms
\[a _{3}=a _{2}+5=(a _{1}+5)+5=8+5+5=18\]
Now what are you doing? I start with the 8 and each time I go to the next number in the sequence, I add 5 to the previous. So the subscript on the a tells me how many TIMES I'm ADDING 5
Restarting at \[a _{0}= 8\]
\[a _{1}=a _{0}+5(1)\]
\[a _{2}=a _{1}+5=a _{0}+5+5=a _{0}+5(2)\]
Notice that the number that you multiply 5 by is the same as the subscript. So in the end,
\[a _{n}=8+5(n)\]