The thirty-second term is 143
Further explanation:
As it is already given that the given sequence is an arithmetic sequence
We have to find the common difference first
So,
[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 -12
The 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 143
Keywords: Common difference, Arithmetic Sequence
Learn more about arithmetic sequence at:
- brainly.com/question/10879401
- brainly.com/question/10940255
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