If the 6th term of an arithmetic
progression is 11 and the first
term is 1, find the common
difference.
A. 3
B. 5
C. -2
D. 2
The formula to find the nth term of an arithmetic progression is given by:
\[a_n = a + (n-1)d\]
where \(a\) is the first term, \(n\) is the term number, and \(d\) is the common difference.
In this case, we have the following information:
The 6th term (\(a_6\)) is 11.
The first term (\(a\)) is 1.
Substituting these values into the formula, we get:
\[11 = 1 + (6-1)d\]
\[11 = 1 + 5d\]
Simplifying this equation, we have:
\[10 = 5d\]
\[d = 2\]
Therefore, the common difference is 2.
The correct answer is D. 2
To find the common difference in an arithmetic progression, we can use the formula:
𝑑 = (𝑡𝑛 − 𝑡1)/(𝑛 − 1)
Where 𝑡𝑛 is the value of the nth term, 𝑡1 is the value of the first term, and 𝑑 is the common difference.
Given that the 6th term (𝑡6) is 11 and the first term (𝑡1) is 1, we can substitute these values into the formula and solve for 𝑑.
𝑑 = (𝑡6 − 𝑡1)/(6 − 1)
= (11 − 1)/(6 − 1)
= 10/5
= 2
Therefore, the common difference is 2.
Answer: D. 2