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Sagot :
Solution:
Given:
First term = 10
Each new term is 5/2 times the previous term.
This implies that;
[tex]\begin{gathered} first\text{ term, }a=10 \\ second\text{ term}=\frac{5}{2}\times10=25 \\ third\text{ term}=\frac{5}{2}\times25=62.5 \\ fourth\text{ term}=\frac{5}{2}\times62.5=156.25 \end{gathered}[/tex]Calculate the common ratio between the successive terms,
[tex]\begin{gathered} \frac{25}{10}=\frac{62.5}{25}=\frac{156.25}{62.5}=2.5 \\ \\ Hence,\text{ }r=2.5 \end{gathered}[/tex]Since the successive terms are increasing by a common ratio, the sequence is a geometric sequence.
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