Sure, let's find the nth term of the given sequence: 7, 10, 13, 16, ...
This sequence is an arithmetic sequence because the difference between consecutive terms is constant. In an arithmetic sequence, the nth term can be found using the formula:
[tex]\[ \text{nth term} = a + (n - 1) \cdot d \][/tex]
where:
- [tex]\( a \)[/tex] is the first term of the sequence,
- [tex]\( d \)[/tex] is the common difference between the terms,
- [tex]\( n \)[/tex] is the position of the term in the sequence.
Let's identify these values from the given sequence:
- The first term [tex]\( a \)[/tex] is 7.
- The common difference [tex]\( d \)[/tex] is the difference between any two consecutive terms. For example, [tex]\( 10 - 7 = 3 \)[/tex] or [tex]\( 13 - 10 = 3 \)[/tex], so [tex]\( d = 3 \)[/tex].
Now, we just need to specify the value of [tex]\( n \)[/tex] to find the nth term.
Let's assume we need to find the 5th term in the sequence (i.e., [tex]\( n = 5 \)[/tex]):
1. Plug in the values into the formula:
[tex]\[ \text{5th term} = 7 + (5 - 1) \cdot 3 \][/tex]
2. Simplify inside the parentheses first:
[tex]\[ 5 - 1 = 4 \][/tex]
3. Then multiply by the common difference:
[tex]\[ 4 \cdot 3 = 12 \][/tex]
4. Finally, add the result to the first term:
[tex]\[ 7 + 12 = 19 \][/tex]
So, the 5th term of the sequence is [tex]\( 19 \)[/tex].
