need to calculate sum of 3 consecutive terms of arithmetic sequence x+4,3x,13x-2

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The terms x + 4, 3x and 13x - 2 are consecutive terms of an arithmetic progression. So we know that they have a common difference

13x - 2 - 3x = 3x - x - 4

=> 10x - 2 = 2x - 4

=> 8x = -2

=> x = -1/4

So the three given terms are -1/4 + 4 = 15/4

3* -1/4 = -3/4

13*(-1/4) - 2 = -21/4

The sum of the three terms is 15/4 - 3/4 - 21/4 = -9/4

The required result is -9/4

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