Given that 11,m,n is an AP. Find the value of m and n
To find the value of m and n, we need more information about the arithmetic progression. The given information "11, m, n" only tells us the first three terms of the sequence. Without knowing the common difference or any other terms in the sequence, we cannot determine the values of m and n.
To find the values of m and n in the arithmetic progression 11, m, n, we need more information. An arithmetic progression (AP) consists of a sequence of numbers in which the difference between any two consecutive terms is constant.
Without additional information about the common difference (d) or any other relationship between the variables, we cannot determine the exact values of m and n.
To find the values of m and n in the arithmetic progression (AP) 11, m, n, we need some additional information or equations. In an AP, the common difference (d) is the constant difference between any two consecutive terms.
Let's assume that the common difference (d) between the terms is the same throughout the AP. Therefore, we can write:
m = 11 + d (Equation 1)
n = m + d (Equation 2)
Now, we have two equations (Equation 1 and Equation 2) and two unknowns (m and n), which means we can solve for the values.
To proceed, we need more information or equations, such as the difference (d) or the values of any two terms. Please provide any additional details or constraints to find the specific values of m and n in the AP.
The fourth term of an AP is 1 less than twice the second term. If the sixth term is 7. Find the
First term
Let's denote the first term of the arithmetic progression as a, and the common difference as d.
Based on the given information, we can create the following equations:
Fourth term: a + 3d = 2(a + d) - 1
Sixth term: a + 5d = 7
Simplifying the equations:
a + 3d = 2a + 2d - 1
-a - d = -1 ........... (Equation 1)
a + 5d = 7 ........... (Equation 2)
To solve these equations, we can use substitution or elimination method.
Using the elimination method, let's multiply Equation 1 by 5 and Equation 2 by -1:
-5a - 5d = -5
-a - d = -1
By adding these two equations, we get:
-6a - 6d = -6
a + d = 1 .................(Equation 3)
Now, we have a system of equations with equations 2 and 3, which can be solved simultaneously.
Adding Equation 2 and Equation 3, we get:
2a + 6d = 8
Now, let's subtract Equation 1 from Equation 2:
-4d = 0
d = 0
Substituting the value of d into Equation 3, we get:
a + 0 = 1
a = 1
Therefore, the first term of the arithmetic progression is 1.