Lewis Harvey

2021-03-02

Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution.
a. $\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$
b. $3,8,13,18,...,48$

Liyana Mansell

Skilled2021-03-03Added 97 answers

Step 1
Given the sequence $(a)\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$
Common difference, $d={t}_{1}-{t}_{2}=\frac{2}{9}-\frac{1}{3}=\frac{-1}{3}\ne {t}_{4}-{t}_{3}=\frac{-5}{81}$
The sequence (a) is not arithmetic .
Common ratio $r=\frac{{t}_{2}}{{t}_{1}}=\frac{3}{2}\ne \frac{7}{2}=\frac{{t}_{3}}{{t}_{2}}$
The sequence (a) is not geometric.
The given sequence is none of the above mentioned types.
$ulO(a)\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$
Step 2
$(b)3,8,13,18,...48$
Common difference, $d={t}_{1}-{t}_{2}=8-3=-5={t}_{3}-{t}_{2}=13-8=-5={t}_{4}-{t}_{3}=-5=.....$
The given sequence (b) is arithmetic.
$ulA(b)3,8,13,18,...48$

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