What is the thirty-second term of the arithmetic sequence -12, -7, -2, 3, ... ? Show your work.

Accepted Solution

The thirty-second term is 143Further explanation:As it is already given that the given sequence is an arithmetic sequenceWe have to find the common difference firstSo,[tex]a_1=-12\\a_2=-7\\a_3=-2\\a_4=3[/tex][tex]d=a_2-a_1=-7-(-12)=-7+12=5\\a_3-a_2=-2-(-7)=-2+7=5[/tex]The common difference is 5.And first term is -12The explicit formula for arithmetic sequence is:[tex]a_n=a_1+(n-1)d\\Here,\\a_n\ is\ nth\ term\\a_1\ is\ first\ term\\d\ is\ common\ difference[/tex]Putting the values in the formula[tex]a_n=-12+(n-1)(5)\\a_n=-12+5n-5\\a_n=-17+5n[/tex]Putting n=32 in explicit formula[tex]a_{32}=-17+5(32)\\=-17+160\\=143[/tex]The thirty-second term is 143Keywords: Common difference, Arithmetic SequenceLearn more about arithmetic sequence at:brainly.com/question/10879401brainly.com/question/10940255#LearnwithBrainly