# Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37.an = -2 (n-)an = -2 (n-1)(5)an = 2 (n-)an = [Solved] Choice A is appropriate Common rule for arithmetic sequence with and is; Step-by-step clarification: Arithmetic sequence states {that a} sequence the place the distinction between every successive pair of phrases is similar. The overall rule for the arithmetic sequence is given by; the place a represents the primary time period d represents the frequent distinction and n represents the variety of phrases. Given: and a (3-1)d = -12 [Using arithmetic sequence rule] a 2nd = -12 or we are able to write this as; a = -12 2nd  Equally, for now we have; a 7d = -37  Substitute equation  into  to resolve for d; -12 2nd 7d = -37 Mix like phrases; -12 5d = -37 Add each side 12 we get; -12 5d 12 = -37 12 Simplify: 5d = -25 Divide each side by 5 we get; d = -5 Substitute the worth of d in equation  to resolve for a; a = -2(-5) 12 a = 10 -12 = -2 a = -2 subsequently, the overall rule for the arithmetic sequence with and is,

we all know the third time period is -12, so the primary one needs to be -12 5 5, undoing the -5s, so the primary time period is -2.

Choice A is appropriate Common rule for arithmetic sequence with and is; Step-by-step clarification: Arithmetic sequence states {that a} sequence the place the distinction between every successive pair of phrases is similar. The overall rule for the arithmetic sequence is given by; the place a represents the primary time period d represents the frequent distinction and n represents the variety of phrases. Given: and a (3-1)d = -12 [Using arithmetic sequence rule] a 2nd = -12 or we are able to write this as; a = -12 2nd  Equally, for now we have; a 7d = -37  Substitute equation  into  to resolve for d; -12 2nd 7d = -37 Mix like phrases; -12 5d = -37 Add each side 12 we get; -12 5d 12 = -37 12 Simplify: 5d = -25 Divide each side by 5 we get; d = -5 Substitute the worth of d in equation  to resolve for a; a = -2(-5) 12 a = 10 -12 = -2 a = -2 subsequently, the overall rule for the arithmetic sequence with and is,

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