The 12th term of the arithmetic progression 2, 5, 8 is 35.
Understanding Arithmetic Progressions
An arithmetic progression (AP) is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference. The formula to find the nth term of an AP is:
an = a + (n - 1)d
Where:
- an is the nth term
- a is the first term
- n is the term number
- d is the common difference
Applying the Formula
In the given arithmetic progression 2, 5, 8:
- The first term (a) is 2.
- The common difference (d) is 5 - 2 = 3.
- We are looking for the 12th term, so n = 12.
Using the formula, we can calculate the 12th term:
a12 = 2 + (12 - 1) 3
a12 = 2 + (11) 3
a12 = 2 + 33
a12 = 35
Reference Verification
According to the provided reference, the 12th term of the given arithmetic progression is 35. This confirms our calculation. The reference indicates:
Here, the first term (a) is 2, the common difference (d) is 3, and we want to find the 12th term (n = 12). Therefore, the 12th term of the given arithmetic progression is 35.
Conclusion
Therefore, by using the arithmetic progression formula and verifying with the reference, the 12th term of the arithmetic progression 2, 5, 8 is indeed 35.
