Answer:
193
Step-by-step explanation:
To find the 50th term of the sequence, an explicit equation would be more useful because it directly calculates the value of any term without having to calculate all the preceding terms.
Let's examine the given sequence: -3, 1, 5, 9. We can observe that each term is increasing by 4.
To find the explicit equation for the nth term of the sequence, we can use the formula for the nth term of an arithmetic sequence:
�
�
=
�
1
+
(
�
−
1
)
⋅
�
a
n
=a
1
+(n−1)⋅d
where:
�
�
a
n
is the nth term,
�
1
a
1
is the first term of the sequence,
�
n is the term number, and
�
d is the common difference between consecutive terms.
In this case:
�
1
=
−
3
a
1
=−3,
�
=
4
d=4.
Substituting these values into the formula, we get:
�
�
=
−
3
+
(
�
−
1
)
⋅
4
a
n
=−3+(n−1)⋅4
Now, we can find the 50th term (
�
50
a
50
) by substituting
�
=
50
n=50 into the equation:
�
50
=
−
3
+
(
50
−
1
)
⋅
4
a
50
=−3+(50−1)⋅4
�
50
=
−
3
+
49
⋅
4
a
50
=−3+49⋅4
�
50
=
−
3
+
196
a
50
=−3+196
�
50
=
193
a
50
=193
Therefore, the 50th term of the sequence is 193.
