The sum of three consecutive terms x,y and z of an arithmetic progression is 45. If y=½ (x + z), find the value of y
wrong again. We know that for any three terms of an AP, y = (x+z)/2
Since x+y+z = 45, the middle term is 45/3 = 15
Apologies for the error.
You are correct. According to the given information, the sum of three consecutive terms x, y, and z of an arithmetic progression is 45, and we know that y = (x + z)/2.
Let's solve for y:
x + y + z = 45
Substituting y = (x + z)/2:
x + (x + z)/2 + z = 45
Multiplying through by 2 to get rid of the denominator:
2x + x + z + 2z = 90
3x + 3z = 90
Dividing through by 3:
x + z = 30
Since y = (x + z)/2:
y = (30)/2
y = 15
Therefore, the value of y is 15.
Let's assume that the first term of the arithmetic progression is a, and the common difference is d.
Therefore, the three terms of the arithmetic progression are:
x = a
y = a + d
z = a + 2d
Given that y = 1/2 (x + z), we can substitute the values of x and z:
a + d = 1/2 (a + a + 2d)
a + d = 1/2 (2a + 2d)
a + d = a + d
This equation is always true, which means that any value of a and d will satisfy the condition.
Therefore, we cannot determine the exact value of y.