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Formula Used:

We are going to use the formula of arithmetic progression, which is:

\[{a_n} = a + \left( {n - 1} \right)d\] , where \[{a_n}\] is the first term, \[a\] is the first term and \[d\] is the common difference.

The given days are Monday, Tuesday, Wednesday, Thursday, and Friday.

So, we take the middle day (Wednesday) as the base day and we are going to represent the other days with respect to Wednesday.

Now, let the temperature on Wednesday be \[a\] and since it forms an arithmetic progression, let the common difference be \[d\] .

So, the temperature on the other days is:

Monday: \[a - 2d\] Tuesday: \[a - d\] Wednesday: \[a\] Thursday: \[a + d\] Friday: \[a + 2d\]

Now, according two the first given information, we have:

\[a - 2d + a - d + a = 0\]

or, \[3a - 3d = 0\] (i)

Then, with the second piece of information, we have:

\[a + d + a + 2d = 15\]

or, \[2a + 3d = 15\] (ii)

Adding equations (i) and (ii),

\[5a = 15\]

or, \[a = 3\]

Putting \[a = 3\] in equation (i) we get,

\[d = 3\]

Hence, the temperature on each day is:

Monday: \[3 - 2 \times 3 = - 3^\circ \]

Tuesday: \[3 - 3 = 0^\circ \]

Wednesday: \[3^\circ \]

Thursday: \[3 + 3 = 6^\circ \]

and, Friday: \[3 + 6 = 9^\circ \]

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