If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.
Answer Details
To find the common difference of the arithmetic progression, we can use the formula:
nth term = a + (n - 1)d
where a is the first term, d is the common difference, and n is the term number.
In this case, we know that the first term is 1, and the sixth term is 11. So we can plug these values into the formula:
11 = 1 + (6 - 1)d
Simplifying the right-hand side, we get:
11 = 1 + 5d
Subtracting 1 from both sides, we get:
10 = 5d
Dividing both sides by 5, we get:
d = 2
Therefore, the common difference of the arithmetic progression is 2.