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3 years ago

Help please thank you

Mathematics

1 answer:

svp [43]3 years ago

8 0

Answer:

The third is an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence means we add the same amount each time as n increases by 1

In the first, we add -6 then -12, then -24 so it is not arithmetic

In the second we add 2 then 4 then 6 then 8

In the third, we add -1.4 each time

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irakobra [83]

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

anzhelika [568]

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:

#LearnwithBrainly

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