write a possible explicit rule for the nth term of each sequence

1.5 , 3 , 4.5 , 6, 7.5

Question

write a possible explicit rule for the nth term of each sequence

1.5 , 3 , 4.5 , 6, 7.5

reemii · Answer

you have to find out if the sequence is rather an arithmetic sequence or a geometric sequence ("do I add something at every step?" VS "do I multiply by some number at every step?")

what do you think here?

anonymous · Answer

add 1.5 every step

hartnn · Answer

thats correct! so this is an arithmetic sequence 

since we add 1.5 every step, d = common difference = 1.5 
a1 = 1st term = 1.5

just use this formula
$\Large a_n = a_1 + (n-1)d$

anonymous · Answer

an= 1.5 + (n-1)1.5

hartnn · Answer

thats correct :) 
now simplify it

hartnn · Answer

not actually....
distribute 1.5 to (n-1)

$1.5(n-1) = 1.5 \times n - 1.5 \times 1$
got that ??

hartnn · Answer

now try to simplify again

anonymous · Answer

i dont know , im hopeless ;o

hartnn · Answer

$a_n = 1.5 +1.5n -1.5$
look what gets cancelled!

reemii · Answer

even though it's not really asked (" write a possible explicit formula .."), it's nice sometimes to see that it can be written in a very simple form.

$ 1.5 +  (n-1)\times 1.5 = 1.5 + n\times1.5 - 1.5 = n\times 1.5$.

anonymous · Answer

you call that very simple ? i call that Spanish.

hartnn · Answer

did you notice 1.5 -1.5 becoming 0 
?

anonymous · Answer

so its an = o + 1.5n

reemii · Answer

correct

hartnn · Answer

which is just 1.5n !

hartnn · Answer

so, $a_n = 1.5n$

hartnn · Answer

thats it! :)

reemii · Answer

however if you stick with 1.5+ (n-1)1.5, it's just as correct.

anonymous · Answer

thanks , even tho you guys probably got irritated ... sorry though.!! <3

hartnn · Answer

no problem, you're learning!
welcome ^_^