Certainly! Let's find the 91st term in the arithmetic sequence 4, 6, 8, ...
In an arithmetic sequence, each term after the first is found by adding a constant difference to the previous term. The general formula to find the nth term of an arithmetic sequence is:
[tex]\[ a_n = a_1 + (n - 1) \cdot d \][/tex]
Where:
- [tex]\( a_n \)[/tex] is the nth term we want to find.
- [tex]\( a_1 \)[/tex] is the first term of the sequence.
- [tex]\( d \)[/tex] is the common difference between the terms.
- [tex]\( n \)[/tex] is the term number.
Given:
- [tex]\( a_1 = 4 \)[/tex]
- [tex]\( d = 6 - 4 = 2 \)[/tex]
We need to find the 91st term ([tex]\( n = 91 \)[/tex]).
Now let's substitute the given values into our formula:
[tex]\[ a_{91} = 4 + (91 - 1) \cdot 2 \][/tex]
First, calculate [tex]\( 91 - 1 \)[/tex]:
[tex]\[ 91 - 1 = 90 \][/tex]
Next, multiply that result by the common difference [tex]\( d \)[/tex]:
[tex]\[ 90 \cdot 2 = 180 \][/tex]
Finally, add this result to the first term [tex]\( a_1 \)[/tex]:
[tex]\[ 4 + 180 = 184 \][/tex]
So, the 91st term of the sequence is:
[tex]\[ a_{91} = 184 \][/tex]
