Understanding Geometric Sequences

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Math › Understanding Geometric Sequences

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Which of the following is a geometric sequence?

$t_{0}=4$

$t_{n}=t_{n-1}\times 3$

$t_{0}=5$

$t_{n}=t_{n-1}+3$

$t_{0}=2$

$t_{n} = t_{n-1}^{6}$

$t_{0}=10$

$t_{n}=t_{n-1}+5$

$t_{0}=4$

$t_{n}=t_{n-1}+3.4$

Explanation

A geometric sequence is one in which the next term is found by mutlplying the previous term by a particular constant. Thus, we look for an implicit definition which involves multiplication of the previous term. The only possibility is:

$t_{0}=4$

$t_{n}=t_{n-1}\times 3$

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