tfind the term of two middle most term of ap -4/3,-1,-2/3,........13/3
well, considering that -1 = -3/3, what about
-4, -3, -2,...,13
same thing. Just keep adding 1.
To find the two middlemost terms of an arithmetic progression ("-4/3, -1, -2/3, ..., 13/3"), we need to determine the total number of terms and then locate the two terms that occupy the middle positions.
First, let's find the number of terms in the arithmetic progression. The general formula to find the number of terms in an arithmetic progression is given by:
\(n = \frac{{a_n - a_1}}{{d}} + 1\)
Where:
\(n\) = number of terms
\(a_n\) = last term of the sequence
\(a_1\) = first term of the sequence
\(d\) = common difference of the arithmetic progression
In this case, the first term (\(a_1\)) is -4/3, the last term (\(a_n\)) is 13/3, and common difference (\(d\)) is the difference between any two successive terms, which is 1/3.
Plugging these values into the formula:
\(n = \frac{{13/3 - (-4/3)}}{{1/3}} + 1\)
\(n = \frac{{17/3}}{{1/3}} + 1\)
\(n = 17 + 1\)
\(n = 18\)
So, the arithmetic progression has a total of 18 terms.
Now, to find the two middlemost terms, we need to locate the terms at positions (n+1)/2 and (n+1)/2 + 1.
In this case, \(n\) is 18, so the middle positions would be (18+1)/2 = 9 and (18+1)/2 + 1 = 10.
Therefore, the two middlemost terms of the given arithmetic progression are the 9th and 10th terms.