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.