To find the nth term of an arithmetic sequence , use the formula:
an=a1+(n−1)da_n=a_1+(n-1)dan=a1+(n−1)d
where:
- ana_nan is the nth term you want to find,
- a1a_1a1 is the first term of the sequence,
- nnn is the position of the term in the sequence,
- ddd is the common difference between consecutive terms (the amount added or subtracted each time).
Steps to find the nth term:
- Identify the first term a1a_1a1.
- Determine the common difference ddd by subtracting any term from the term that follows it.
- Substitute a1a_1a1, ddd, and nnn into the formula.
- Simplify to find the value of the nth term.
Example:
Given the sequence: 3, 9, 15, 21, 27, ...
- First term a1=3a_1=3a1=3
- Common difference d=9−3=6d=9-3=6d=9−3=6
- Find the 25th term (n=25n=25n=25):
a25=3+(25−1)×6=3+24×6=3+144=147a_{25}=3+(25-1)\times 6=3+24\times 6=3+144=147a25=3+(25−1)×6=3+24×6=3+144=147
So, the 25th term is 147
. This formula works for both increasing and decreasing sequences (if ddd is negative, the sequence decreases)
