41
a) Find the nth term of the arithmetic
sequence 1, 11, 21, 31, 41,

b) Find the 100th term

c) Is 205 in the sequence? How do you
know?

d) Which term in the sequence is 161?
d

a) 1 + ( 10x - 10 )

b) 991

c) will not be included

d) 17th

Step-by-step explanation:

a) you can calculate the nth term of the arithmetic sequence by using an equation of 1 + ( 10x - 10 ), where x represents the term.

- For the 3rd term, input 3 into the equation, 1 + ( 10 (3) - 10 ), then evaluate, which equals to 21.

b) Simply input 100 into "x" for the answer,

= 1 + ( 10 ( 100 ) - 10 )

= 1 + ( 1000 - 10 )

= 1 + 990

= 991

c) Immediately, you can determine that 205 will not be included in the sequence simply by looking at the last digit the number ends with. Since it ends with a 5, whereas all the terms in the sequence end with 1, the number is not included.

d) we can get 161 by using algebra, inputing 161 in for what the equation equals to and solve for "x,"

161 = 1 + ( 10x - 10 )

161 - 1 = 10x - 10

160 + 10 = 10x

170 = 10x

10      10

17 = x

The 17th term will have 161 in its sequence.

idc

step-by-step explanation:

idk

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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