How do I find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. #A_n = 12 + (n–1)(3)# ?

Question

3, 24, 27 12, 21, 39 12, 24, 42 0, 9, 27

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Answer 1 · 2018-07-17T05:24:34

#A_1 = 12; " "A_4 = 21; " "A_10 = 39#

Given: An arithmetic sequence with rule #A_n = 12 + (n-1)(3)#

Arithmetic sequences have a general rule: #A_n = A_1 + (n-1)d#

where #d# = common difference between consecutive terms.

#A_1 = 12 + (1-1)(3) = 12 + 0 = 12#

#A_4 = 12 + (4-1)(3) = 12 + 3(3) = 21#

#A_10 = 12 + (10-1)(3) = 12 + 27 = 39#