(a) An arithmetic progression contains 25 terms and the first term is −15. The sum of all the terms in the progression is 525. Calculate the common difference of the progression,

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The data given in the question as follows.

`a = -15`

`n = 25`

`S_n = 525`

The sum of the arithmetic series given as;

`S_n = (n/2) (2a+(n-1)d)`

`525 = (25/2) (-15*2 + (25-1)d)`

`1050 = 25(-30+24d)`

`42+30 = 24d`

`d=3`

So the common difference is 3.

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