1) Determine whether each recursive formula defines an arithmetic sequence,if it is arithmetic state the first five terms
a) T^1=1, t^n =2t^n-1-n+2
how do we know if its arithmetic ? Pleasehelp
The nth term, $\displaystyle t_n$, of a geometric sequence, with first term a and common multiple r, is $\displaystyle t_n= ar^{n-1}$. Surely you knew that?
So the 5 term is $\displaystyle ar^4= 45$ and the 8th term is $\displaystyle ar^7= 360$. Use those to determine the values of a and r and the finnd $\displaystyle a_{20}= ar^{19}$.
Don't worry: if you do, the paper won't burst into flames. In other words, why don't you try?
ar^{7} = 360 and ar^{4} = 45. Divide the first equation by the second one, i.e., divide the left-hand sides and then the right-hand sides and equate the results. Alternatively, express a from the second equation: a = 45 / r^{4} and substitute it into the first equation.