Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37. an = -2 + (n-1)(-5) an = -2 + (n-1)(5) an = 2 + (n-1)(-5) an = 2 + (n-1)(5)

Answer:Option A is correctGeneral rule for arithmetic sequence with [tex]a_3 = -12[/tex] and [tex]a_8 = -37[/tex] is; [tex]a_n=-2+(n-1)(-5)[/tex]Step-by-step explanation:Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same. The general rule for the arithmetic sequence is given by; [tex]a_n=a+(n-1)d[/tex] wherea represents the first termd represents the common difference and n represents the number of terms.Given: [tex]a_3 = -12[/tex] and [tex]a_8 = -37[/tex][tex]a_3 = -12[/tex]a+(3-1)d = -12                    [Using arithmetic sequence rule]a + 2d = -12                or we can write this as;a = -12 - 2d                                       ......[1]Similarly, for  [tex]a_8 = -37[/tex] we have;[tex]a+(8-1)d = -37[/tex]a+7d = -37                 ......[2]Substitute equation [1] into [2] to solve for d;-12 - 2d +7d = -37Combine like terms;-12 + 5d = -37Add both sides 12 we get;-12 + 5d + 12 = -37 + 12Simplify:5d =  -25Divide both sides by 5 we get;d = -5Substitute the value of d in equation [1] to solve for a;a = -2(-5) - 12a = 10 -12 = -2∴ a = -2therefore, the general rule for the arithmetic sequence with [tex]a_3 = -12[/tex] and [tex]a_8 = -37[/tex] is,  [tex]a_n=-2+(n-1)(-5)[/tex]