The fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is [tex]a_{n} = a_{n -1} 5[/tex].
According to the given question.
We have a formula for finding the general term of a sequence is
[tex]a_{n} = a_{n -1} 5[/tex]
Also,
The first term of the sequence, [tex]a_{1} = 2[/tex]
Therefore,
The fifth term of the sequence is given by
[tex]a_{5} = a_{5-1} 5[/tex]
⇒ [tex]a_{5} = a_{4} 5[/tex]
⇒ [tex]a_{5} = (a_{4-1}5) 5[/tex]
⇒ [tex]a_{5} = a_{3}25[/tex]
⇒ [tex]a_{5} = (a_{3-1}5) 25[/tex]
⇒ [tex]a_{5} = a_{2} 125[/tex]
⇒ [tex]a_{5} = a_{2 -1} (5)125[/tex]
⇒ [tex]a_{5} = a_{1} 625[/tex]
⇒ [tex]a_{5} = 2(625)[/tex]
⇒ [tex]a_{5} = 1250[/tex]
Hence, the fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is [tex]a_{n} = a_{n -1} 5[/tex].
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