# 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

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. $3,8,13,18,...,48$
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Step 1 Given the sequence $\left(a\right)\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$ 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. $ulO\left(a\right)\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$ Step 2 $\left(b\right)3,8,13,18,...48$ 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. $ulA\left(b\right)3,8,13,18,...48$