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katrin2010 [14]
2 years ago
7

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

Mathematics
1 answer:
anzhelika [568]2 years ago
6 0

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,

a_1=-12\\a_2=-7\\a_3=-2\\a_4=3

d=a_2-a_1=-7-(-12)=-7+12=5\\a_3-a_2=-2-(-7)=-2+7=5

The common difference is 5.

And first term is -12

The explicit formula for arithmetic sequence is:

a_n=a_1+(n-1)d\\Here,\\a_n\ is\ nth\ term\\a_1\ is\ first\ term\\d\ is\ common\ difference

Putting the values in the formula

a_n=-12+(n-1)(5)\\a_n=-12+5n-5\\a_n=-17+5n

Putting n=32 in explicit formula

a_{32}=-17+5(32)\\=-17+160\\=143

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

#LearnwithBrainly

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