The first term of an arithmetic progression is 12 and the sum of the first 16 terms

Question:

The first term of an arithmetic progression is 12 and the sum of the first 16 terms is 282.

a. Find the common difference of this progression.

The first, fifth and nth term of this arithmetic progression are the first, second and third term respectively of a geometric progression.

b. Find the common ratio of the geometric progresion and the value of n.

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