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There are 2 Arithmetic Progression series :
A1 = 1,5,9,...............481
A2 = 5,11,17..............479
What is the sum of common terms of the 2 Arithmetic Progressions?
Correct answer is '9560'. Can you explain this answer?
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Verified Answer
There are 2 Arithmetic Progression series :A1= 1,5,9,...............48...
A1 has a common difference of 4 whereas A2 = 6
Let us identify the first common term. Visually we can see that the first term will be 5
The series formed by taking the common terms of the series will also be an AP with the common difference of the A.P = lcm(4,6) = 12
nth term of this series will be = 5+(n−1)12
The maximum possible value of the last common number will be 479
Therefore, 5+(n−1)12 ≤ 479
(n−1)12 ≤ 474
(n−1) ≤ 5474=39.5
(n) ≤ 40.5
Therefore n = 40 is the number of terms in the resulting series
Sum of all the common 40 terms = 40/2(2(5)+(40−1)12)
Sum of all the common 40 terms = 20(10+39× 12)
Sum of all the common 40 terms = 20(478) = 9560
Most Upvoted Answer
There are 2 Arithmetic Progression series :A1= 1,5,9,...............48...
Given:
Arithmetic Progression A1: 1, 5, 9, ..., 481
Arithmetic Progression A2: 5, 11, 17, ..., 479
To Find:
The sum of common terms of the two Arithmetic Progressions A1 and A2.
Approach:
To find the sum of common terms of two Arithmetic Progressions, we need to first find the number of common terms and then calculate their sum.
Step 1: Finding the number of common terms:
Let's denote the common terms as 'x'.
In Arithmetic Progression A1, the first term is 1 and the common difference is 4.
In Arithmetic Progression A2, the first term is 5 and the common difference is 6.
To find the number of common terms, we need to equate the terms of both progressions and solve for 'x':
1 + (x - 1) * 4 = 5 + (x - 1) * 6
Simplifying the equation,
4x - 3 = 6x - 1
2x = 2
x = 1
Therefore, there is only one common term in the two progressions.
Step 2: Calculating the sum of the common terms:
Since there is only one common term, we can directly calculate its value.
The common term can be found by substituting 'x' into the equation for A1:
A1 = 1 + (1 - 1) * 4 = 1 + 0 * 4 = 1
The sum of the common terms can be calculated by multiplying the common term by the number of common terms:
Sum of common terms = 1 * 1 = 1
Answer:
The sum of common terms of the two Arithmetic Progressions A1 and A2 is 1.
Arithmetic Progression A1: 1, 5, 9, ..., 481
Arithmetic Progression A2: 5, 11, 17, ..., 479
To Find:
The sum of common terms of the two Arithmetic Progressions A1 and A2.
Approach:
To find the sum of common terms of two Arithmetic Progressions, we need to first find the number of common terms and then calculate their sum.
Step 1: Finding the number of common terms:
Let's denote the common terms as 'x'.
In Arithmetic Progression A1, the first term is 1 and the common difference is 4.
In Arithmetic Progression A2, the first term is 5 and the common difference is 6.
To find the number of common terms, we need to equate the terms of both progressions and solve for 'x':
1 + (x - 1) * 4 = 5 + (x - 1) * 6
Simplifying the equation,
4x - 3 = 6x - 1
2x = 2
x = 1
Therefore, there is only one common term in the two progressions.
Step 2: Calculating the sum of the common terms:
Since there is only one common term, we can directly calculate its value.
The common term can be found by substituting 'x' into the equation for A1:
A1 = 1 + (1 - 1) * 4 = 1 + 0 * 4 = 1
The sum of the common terms can be calculated by multiplying the common term by the number of common terms:
Sum of common terms = 1 * 1 = 1
Answer:
The sum of common terms of the two Arithmetic Progressions A1 and A2 is 1.
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There are 2 Arithmetic Progression series :A1= 1,5,9,...............481A2= 5,11,17..............479What is the sum of common terms of the 2 Arithmetic Progressions?Correct answer is '9560'. Can you explain this answer?
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