Question

If a1=5 and an= -5an-1 then find the value of a5.

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Answer 1

Answer:

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:

$a_1=5$

$a_n=-5a_{n-1}$

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

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

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

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

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

The value of a5 is 3125