Question

Express the terms of the following geometric sequence recursively,3,1,A ty = 3 and tn = (tn–1) – 3, for n > 2ОВ.t1 = 3 and tn = }(tn-1), for n > 2OC t1 = 3 and tn = tn-1 + žr, for n > 2OD. t1 = 3 and ty = ty-1 - 2n, for n > 2

Answer 1

Given the sequence;

$3,1,\frac{1}{3},\frac{1}{9},\frac{1}{27}$

The common ratio r, of a geometric sequence is the ratio between two consecutive terms of a geometric sequence.

$r=\frac{t_2}{t_1}=\frac{1}{3}$

The recursive formular for a geometric sequence is given as;

$\begin{gathered} t_n=r(t_{n-1}),\text{ for n}\ge2 \\ \text{Thus;} \\ t_1=3_{} \\ \text{and t }_n=\frac{1}{3}(t_{n-1}),\text{ for n}\ge2 \end{gathered}$

Thus, the correct option is B