How do you find the next two terms of the geometric sequence $5/2, 5/3, 10/9, ...$ ?

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Answer 1 · 2016-11-09T09:39:38

$20/27, 40/81$

In a GP the next term is obtained by multiplying by $r$ , the common ratio,

Find $r rarr r = T_3/T_2 = T_2/T_1$

$r = 5/3 div 5/2 = 5/3 xx 2/5 = 2/3$

Check: $5/3 xx 2/3 = 10/9$

$T_4 = 10/9 xx 2/3 = 20/27$

$T_5 = 20/27 xx2/3 = 40/81$

How do you find the next two terms of the geometric sequence 5/2, 5/3, 10/9, ...5/2, 5/3, 10/9, ...?