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.

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$r = \frac{t _{n}}{t _{n - 1}} = \frac{- \frac{7 t _{n - 1}}{3}}{t _{n - 1}} = - \frac{7}{3}, n \geq 2$

We have a geometric progression

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

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

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Question ID: mtid-5-stid-8-sqid-1393-qpid-1131