The sum of three consecutive terms of an AP is 72 then what is the middle term
Middle term = a
Three terms: (a-d), a, (a+d) are in A.P.
(a+d) + a + (a-d) = 72
=> 3a + d - d = 72
=> 3a = 72
Solve for a
24
Let's assume that the three consecutive terms of the arithmetic progression (AP) are a-d, a, and a+d, where 'a' is the middle term and 'd' is the common difference.
According to the given information, the sum of these three terms is 72:
(a-d) + a + (a+d) = 72
By combining like terms, we can simplify this equation:
3a = 72
Now, divide both sides of the equation by 3 to solve for 'a':
a = 72/3
a = 24
Therefore, the middle term of the AP is 24.
To find the middle term of an arithmetic progression (AP), we can use the formula for the nth term of an AP:
\[a_n = a + (n-1)d\]
where \(a\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
Let's assume the middle term of the AP is \(a_2\). Then, the sum of the three consecutive terms will be:
\[a_1 + a_2 + a_3 = 72\]
Substituting the formula for \(a_1\) and \(a_3\):
\[a + (1-1)d + a + (2-1)d + a + (3-1)d = 72\]
Simplifying:
\[3a + 3d = 72\]
Dividing both sides of the equation by 3:
\[a + d = 24\]
Since we assumed the middle term is \(a_2\), we can substitute \(a + d\) with the formula \(a_2 = a + d\):
\[a_2 = 24\]
Therefore, the middle term of the AP is 24.