# consecutive terms of a.p.given 3 consecutive unknown terms of a.p., i'm stuck calculating the sum of the 3 terms!

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Expert Answers

justaguide | Certified Educator

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.