The first three terms of an arithematic profgression are x,2x+y and 9x-y.The sum of these three terms is 60.Find the numerical values of x and y.Then,calculate the eleventh term of the progression
if in an AP,
2x+y - x = 9x-y - (2x+y)
x + y = 7x - 2y
3y = 6x
y = 2x
also: x + 2x+y + 9x - y = 60
12x = 60
x = 5 , then
y = 10
so the first term is x or 5
common difference = 2x+y - x
= x+y
= 15
term11 = a+10d = 5 +150 = 155
check:
first 3 terms are:
5 , 20 , 35, ...
is their sum = 60 ? YES
Yup..Thanks a lot!
To find the values of x and y, we need to use the given information that the sum of the three terms is 60.
The sum of an arithmetic progression can be calculated using the formula Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
So, we can write the sum of the three terms as:
60 = (3/2)(2x + 8x) [by substituting a = x, d = 2x - x = x]
60 = (3/2)(10x)
60 = 15x
Now, we can solve for x:
15x = 60
x = 60/15
x = 4
Next, we can substitute the value of x into the second and third terms of the arithmetic progression to find y:
2x + y = 2(4) + y = 8 + y
9x - y = 9(4) - y = 36 - y
Now, we know that the sum of the three terms is 60, so we can write the equation:
x + (2x + y) + (9x - y) = 60
4 + (8 + y) + (36 - y) = 60
4 + 8 + y + 36 - y = 60
48 = 60
This equation is not possible because 48 is not equal to 60. Hence, there is no solution for y in this case.
Since we do not have a value for y, we cannot calculate the eleventh term of the arithmetic progression.