1)Find the first 4 terms defined by tn = 5n + 1      2)Find the next two terms and the recursive formula for the sequence, -5, -2, 1, 4, … .Sequences

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1) You need to find the first 4 terms of a sequence defined by `t_n = 5n + 1` , hence, you should substitute 1,2,3,4 for n such that:

`n =1=>`   `t_1 = 5*1 + 1` => `t_1 = 6`

`n=2 => t_2 = 5*2 + 1 => t_2 = 11`

`n=3 => t_3 = 5*3 + 1 => t_3 = 16`

`n=4 => t_4 = 5*4+1 => t_4 = 21`

Hence, evaluating the 4 terms of the sequence defined by `t_n = 5n + 1`  yields `t_1 = 6 ; t_2 = 11 ; t_3 = 16 ; t_4 = 21` .

2) You should notice that the given sequence is an arithmetic progression since the difference between each two consecutive terms yields 3.

Hence, since the common difference is d=3, you may find the next two terms such that:

`a_5 =a_4 + d => => a_5 = 4 + 3 => a_5 = 7`

`a_6 = a_5 + d => a_6 = 7 + 3 => a_6 = 10`

Hence, evaluating the next two terms under the given conditions yields `a_5 = 7`  and `a_6 = 10` .