Question

Find, showing all working, a formula for the n-th term tn of the sequence (tn) defined by t1 = 5; tn = −7tn−1/3, n ≥ 2.

Answer 1

$$r=\dfrac{t_n}{t_{n-1}}=\dfrac{-\dfrac{7t_{n-1}}{3}}{t_{n-1}}=-\dfrac{7}{3}, n\geq2$$

We have a geometric progression

$$a=t_1=5, r=-\dfrac{7}{3}$$

$$t_n=5(-\dfrac{7}{3})^{n-1}, n\geq2$$