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=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
