Answer:
Explanation:
To find the term of an arithmetic progression (AP) with a common difference of 2, we can use the formula:
�
�
=
�
1
+
(
�
−
1
)
�
a
n
=a
1
+(n−1)d
Where:
�
�
a
n
is the
�
nth term of the AP,
�
1
a
1
is the first term of the AP,
�
n is the position of the term we want to find, and
�
d is the common difference of the AP.
In this case, we have
�
1
=
5
a
1
=5 and
�
=
2
d=2. We want to find the term that is equal to 133. Let's substitute these values into the formula:
133
=
5
+
(
�
−
1
)
⋅
2
133=5+(n−1)⋅2
Simplifying the equation:
133
=
5
+
2
�
−
2
133=5+2n−2
Combining like terms:
133
=
3
+
2
�
133=3+2n
Now, isolate
�
n by subtracting 3 from both sides:
130
=
2
�
130=2n
Dividing both sides by 2:
�
=
65
n=65
Therefore, the term that is equal to 133 in the arithmetic progression 5, 7, 9, 11, 13, ... is the 65th term.