Question

Write a possible explicit rule for the nth term of the sequence. 23.1, 20.2, 17.3, 14.4, 11.5, 8.6, ...

Answer 1

What would the formula be to find the solution to this problem?

Answer 2

find the different between those numbers:
23.1 -20.2 = 2.9
20.2 - 17.3 = 2.9
17.3 - 14.4 = 2.9
14.4 - 11.5 =2.9
11.5 - 8.6 =2.9
.......... so, the formula for this is \[a_n = a_{n-1} -2.9\]
if you need more general formula and understand it, you have to come up with the problem in other way, but I don't think you need it. However, I still give you that formula
\[a_n = 23.1 - n(2.9)\]

Answer 3

the nth term usually starts at 1, not 0

Answer 4

So is an = 23.1 - n(2.9) just an example?..

Answer 5

@amistre64 I am hearing you.

Answer 6

What is a in the equation?

Answer 7

a signifies that this is an element of the set A is all

Answer 8

\[A={\{a_n:n\in Z^+}\}\]

Answer 9

\[A=\{a_1,a_2,a_3,a_4,...,a_k\}\]

Answer 10

So to find the nth term, an would be any of the numbers in the sequence, n being the number in the sequence (ex 6th?)

Answer 11

correct

Answer 12

Okay makes perfect sense now, thank you guys c:

Answer 13

we just have to be cautious when making an explicit, different authors like to start thier ns at 0 or 1

Answer 14

Well you can't have a 0th term

Answer 15

@amistre64 yes, you are right, my prof always ask us start at 0,

Answer 16

you can, especially in banking and interest calculations

Answer 17

@Cookieyumm just notation,

Answer 18

Oh, okay.

Answer 19

if we start at n=1 notice how that the setup is a normal counting processes; the 8th term is n=8

1,2,3,4,5,6,7,8,9,10
------------------------------------

if we start at n=0 notice how that changes the setup; the 8th term is n=8-1

0,1,2,3,4,5,6,7,8,9

Answer 20

Oh, so that's why it's n-1

Answer 21

correct

Answer 22

That definitely clears things up.

Answer 23

good luck ;)

Answer 24

Thank you!