Given the arithmetic sequence 7, 5, 3, 1, -1 Then the recursive rule is [tex]\mathrm{t}_{\mathrm{n}}=\mathrm{t}_{\mathrm{n}-1}-2[/tex]
Solution:
Given that, an arithmetic sequence is 7, 5, 3, 1, - 1
We have to write the recursive rule for the above given arithmetic sequence
Now, let us find the common difference for the above given arithmetic sequence,
Common difference d = any term of sequence – its previous term
d = 5 – 7 = - 2
So, common difference d = - 2
Now, we know that, recursive rule is an equation that gives the next value by performing certain operation on the previous value.
Here for any arithmetic sequence, it will be nth term = (n – 1)th term + common difference
[tex]\begin{array}{l}{\text { Then, } t_{n}=t_{n-1}+d} \\\\ {\rightarrow t_{n}=t_{n-1}+(-2)} \\\\ {\rightarrow t_{n}=t_{n-1}-2}\end{array}[/tex]
Hence, the recursive rule is [tex]\mathrm{t}_{\mathrm{n}}=\mathrm{t}_{\mathrm{n}-1}-2[/tex]
