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Leno4ka [110]
3 years ago
11

Is the sequence geometric if so identify the common ratio 1/3, 2/9, 4/27, 8/81, 16/243

Mathematics
2 answers:
zavuch27 [327]3 years ago
6 0

Answer:

Yes, the given sequence is geometric and the common ratio is \frac{2}{3}.

Step-by-step explanation:

The given sequence is

\frac{1}{3},\frac{2}{9},\frac{4}{27},\frac{8}{81},\frac{16}{243}

If the ratio of all two consecutive terms are same, then the sequence is called geometric.

r=\frac{a_{n+1}}{a_n}

r_1=\frac{\frac{2}{9}}{\frac{1}{3}}=\frac{2}{3}

r_2=\frac{\frac{4}{27}}{\frac{2}{9}}=\frac{2}{3}

r_3=\frac{\frac{8}{81}}{\frac{4}{27}}=\frac{2}{3}

r_4=\frac{\frac{16}{243}}{\frac{8}{81}}=\frac{2}{3}

r_1=r_2=r_3=r_4

Therefore the given sequence is geometric and the common ratio is \frac{2}{3}.

docker41 [41]3 years ago
3 0
Yes it is a geometric sequence and the common ratio is 2/3
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