use y to identify each term in the sequence and n to identify each terms position.   4,8,12,16,...

Expert Answers

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You should notice that the given terms are the consecutive terms of an arithmetic progression, whose common difference is `d =` `8-4=12-8=16-12=...=4.`

You may use the general term formula that helps you to identify each term of progression, such that:

`y_n = y_1 + (n - 1)*d`

Identifying the first term of progression as `y_1 = 4` , yields:

`y_2 = y_1 + (2-1)*4 => y_2 = 4 + 1*4 => y_2 = 8`

`y_3 = y_1 + (3-1)*4 => y_3 = 4 + 2*4 => y_3 = 12`

Hence, the given terms 4,8,12,16,.. represents the terms `y_1,y_2,y_3,y_4,.. ` of an arithmetic progression `(y_n)_(n>=1)` , whose first term is `y_1 = 4` and whose common difference is `d = 4.`

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