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The first three terms of an AP are 3y-1,3y+5and 5y+1 respectively.find the value of y
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The first three terms of an AP are 3y-1,3y+5and 5y+1 respectively.find...
In AP : Difference b/w successive terms=constant
Therefore,3y+5-(3y-1)=5y+1-(3y+5)
3y+5-3y+1=5y+1-3y-5
6=2y-4
10=2y
Therefore,y=5
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The first three terms of an AP are 3y-1,3y+5and 5y+1 respectively.find...
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The first three terms of an AP are 3y-1,3y+5and 5y+1 respectively.find...
Given:
The first three terms of an arithmetic progression (AP) are 3y-1, 3y+5, and 5y+1.
To find:
The value of y.
Solution:
To find the value of y, we can use the property of an arithmetic progression where the difference between consecutive terms is constant.
Step 1: Find the common difference (d)
The common difference (d) can be found by subtracting the second term from the first term, or the third term from the second term.
Using the first two terms:
d = (3y+5) - (3y-1)
= 3y + 5 - 3y + 1
= 6
Step 2: Write the general form of the AP
The general form of an arithmetic progression is given by:
a + (n-1)d
where a is the first term, n is the position of the term, and d is the common difference.
Step 3: Find the first term (a)
From the given information, the first term is 3y-1.
Step 4: Find the second and third terms
The second term is given as 3y+5.
The third term is given as 5y+1.
Step 5: Substitute the values into the general form
Using the first term, common difference, and position of the second term:
3y-1 + (2)(6) = 3y+5
Simplifying the equation:
3y-1 + 12 = 3y+5
3y + 11 = 3y + 5
Subtracting 3y from both sides of the equation:
11 = 5
This is a contradiction, so there is no specific value of y that satisfies the given information.
Conclusion:
There is no value of y that satisfies the given information. The terms 3y-1, 3y+5, and 5y+1 do not form an arithmetic progression.
The first three terms of an arithmetic progression (AP) are 3y-1, 3y+5, and 5y+1.
To find:
The value of y.
Solution:
To find the value of y, we can use the property of an arithmetic progression where the difference between consecutive terms is constant.
Step 1: Find the common difference (d)
The common difference (d) can be found by subtracting the second term from the first term, or the third term from the second term.
Using the first two terms:
d = (3y+5) - (3y-1)
= 3y + 5 - 3y + 1
= 6
Step 2: Write the general form of the AP
The general form of an arithmetic progression is given by:
a + (n-1)d
where a is the first term, n is the position of the term, and d is the common difference.
Step 3: Find the first term (a)
From the given information, the first term is 3y-1.
Step 4: Find the second and third terms
The second term is given as 3y+5.
The third term is given as 5y+1.
Step 5: Substitute the values into the general form
Using the first term, common difference, and position of the second term:
3y-1 + (2)(6) = 3y+5
Simplifying the equation:
3y-1 + 12 = 3y+5
3y + 11 = 3y + 5
Subtracting 3y from both sides of the equation:
11 = 5
This is a contradiction, so there is no specific value of y that satisfies the given information.
Conclusion:
There is no value of y that satisfies the given information. The terms 3y-1, 3y+5, and 5y+1 do not form an arithmetic progression.
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