Arithmetic sequence

In the arithmetic sequence t1, t2, t3,....., tn,......., t1=23 and tn=(tn-1)-3 for each n>1, what is the value of n when tn= -4?

a)-1
b)7
c)10
d)14
e)20


Can you please help me? I don't get this question, i don't know how to solve it, I should substitute what for what? :?

In the arithmetic sequence t1, t2, t3,....., tn,......., t1=23 and tn=(tn-1)-3 for each n>1, what is the value of n when tn= -4?

a)-1
b)7
c)10
d)14
e)20

n...-4...-3...-2...-1...0...1...2...3...4...5...6
tn..38...35..32...29.26.23.20..17.14..11.8

I could be misreading your statement but I get 38 for tn = -4

As I suspected, I misread the problem statement. As already shown,

n....1...2...3...4...5...6...7...8...9...10
tn.23.20.17..14.11..8...5...2..-1....-4

is the correct interpretation. Sorry for the misdirection.

Hello, Alejandra!

In the arithmetic sequence: \(\displaystyle t_1,\,t_2,\,t_3,\,....\,t_n,\;\;t_1\,=\,23\) and \(\displaystyle t_n\:=\:t_{n-1}\,-\,3\) for each \(\displaystyle n\,>\,1\).

What is the value of \(\displaystyle n\) when \(\displaystyle t_n\,=\,-4\) ?

\(\displaystyle a)\;-1\;\;\;\;b)\;7\;\;\;\;c)\;10\;\;\;\;d)\;14\;\;\;\;e)\;20\)

Click to expand...

We are given an arithmetic sequence with first term \(\displaystyle a\,=\,23\) and common difference \(\displaystyle d\,=\,-3\)

The n^th term is: \(\displaystyle \,a_n\:=\:a\,+\,d(n\,-\,1)\;\;\Rightarrow\;\;t_n\:=\:23\,-\,3(n\,-\,1)\)

If \(\displaystyle t_n\,=\,-4\), we have: \(\displaystyle \,23\,-\,3(n\,-\,1)\:=\:-4\)

Solve for \(\displaystyle n\) and get: \(\displaystyle \,n\,=\,10\) . . . answer (c).

Hmmm....I get 10