If a1 = 3 and an = 5an-1 then find the value of a5.
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The value of a5 is 3125

Step-by-step explanation:

Recursive Sequence

It refers to the sequences where each term is given as a rule that depends on one or more of the previous terms, unlike explicit sequences where a general term is given and we can calculate any term without knowing the value of the previous terms, except for the first one.

The sequence is given as:

a_1=5a

1

=5

a_n=-5a_{n-1}a

n

=−5a

n−1

To find the value of a5, we need to find the previous terms first:

a_2=-5a_{1}=-5*5=-25a

2

=−5a

1

=−5∗5=−25

a_3=-5a_{2}=-5*(-25)=125a

3

=−5a

2

=−5∗(−25)=125

a_4=-5a_{3}=-5*125=-625a

4

=−5a

3

=−5∗125=−625

a_5=-5a_{4}=-5*(-625)=3125a

5

=−5a

4

=−5∗(−625)=3125

The value of a5 is 3125

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