What is the 10th term of the sequence "12, 23, 34, 45...."? How do you write an equation for the #n#th term of the sequence?

Answer 1

For #i=10:color(white)(...) a_10= 111#

So for #i=n:color(white)(...) a_i=a_n=12+11(n-1)#

#color(blue)("Test for Arithmetic")#

{23-12 = 11}, {34-23= 11}, {45-34=11}

This is an Arithmetic sequence as all the differences are the same.

Let #a_i# be the #i"'th term"#

Let n be any integer value

#a_1=12# #a_2=12+11# #a_3=12+(2xx11)# #a_4=12+(3xx11)#

and so on

so if we have #a_i=12+11(i-1)# it should work for any #i#
Test: #a_1=12+11(1-1) =12# #a_4=12+11(4-1)=12+33=45#
For #i=10: a_10=12+11(10-1) = 12+99 = 111#
So for #i=n: a_i=a_n=12+11(n-1)#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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