1. Examine the first four terms in each of the following number sequences:

Question

*2, 7, 12, 17 my formula x+5
*7, 21, 63, 189, 567 my formula x(2)+x
*1000, 850, 700, 550 my formula x-150
* –10, –6, –2, 2 my formula x+4

For each sequence, what would be the 20th and 100th term? Explain your reasoning for each.

For which of the sequences would the number 352 be a term? Explain your reasoning.

One of the sequences is different from the other three. Describe what makes the one different and the other three "alike."

Answer 1

All your choices are correct except the 2nd

look at the terms:
7, 21, 63, 189, 567, ...
or
7*1, 7*3, 7*9, 7*27, 7*81

looks like 7* 3^(x-1)

btw, that sequence is the one that different from all the others, because it is NOT an arithmetic sequence.

For the 20th and 100th term, I will do the first, you repeat the same method for the others

for 2 7 12 17 ...
a = 2, d = 5
term 20 = a + 19d
= 2 + 19(5) = 97

term 100 = a + 99d
= 2 + 99(5) = 497

As to 352 being one of the terms?

let the term number be n
term n = a + (n-1)d
2 + (n-1)(5) = 352
5n - 5 = 350
5n = 355
n = 71

yes, 352 is the 71st term in the first sequence
repeat for the 3rd and 4th sequence

testing for the 2nd sequence
7*(3)^(n-1) = 352
3^(n-1) = 352/7
which clearly is NOT a power of 3, so 352 does not belong to the 2nd sequence

Answer 2

7*1, 7*3, 7*9, 7*27, 7*81

looks like 7* 3^(x-1) I don't understand how you got (x-1) can you explain?

Answer 3

The multipliers are

1,3,9,27, ...
As powers of 3, those are 0,1,2,3,...

You can't say 7*3^x because the first term (x=1) has not been multiplied yet.