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Let the three terms of the AP be a , b and c.
Consecutive terms of an AP have a common difference
b = a + d and c = b + d = a + 2d
If you can determine a and d using the relations for the others in terms of a and d, you can determine the sum of the three terms.
For example, consider the problem: Let the sum of the first two terms of an AP be 9 and the sum of the second and third is 15. What is the sum of the 3 consecutive terms.
Here a + b = 9 and b + c = 15
=> a + a + d = 9 and a + d + a + 2d = 15
=> 2a + d = 9 and 2a + 3d = 15
=> 2d = 6
=> d = 3
a = 3
The sum of the three terms is 3a + 3d = 18.
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