Question

Which of the numbers below could be terms in the sequence an = 3n + 16?

A. 64

B. 48

C. 46

D. 61

please please help

Answer 1

I believe the correct answer would be A,C,D, but PLEASe let me know :)

Answer 2

why not test your answer out
math is not about guessing

Answer 3

@nincompoop I don't know how to test out the answer, which is why I'm stuck

Answer 4

You can either:
1. set each answer = to the expression for the sequence and see if the solution is an integer;

or

2. Start listing the sequence, see if those numbers come up when you get to a high enough n.

Answer 5

One way to do it is to rearrange the equation so it looks like this (assume the number you're testing is called b):\[b = 3n + 16\]\[b-16=3n\]\[\frac{b-16}{3} = n\]
Basically, when you plug in a number for b, if it evaluates such that n is an *integer* then b is in the sequence.

Answer 6

@DebbieG if I want to approach this using your 2nd suggestion, how do I start listing the sequence if it is 3n+16? I'm confused about that part

Answer 7

For the 2nd suggestion, you would start with n=0 and plug it in. Then n=1, n=2, etc.

Answer 8

n=1:
3(1)+16=19

n=2:
3(2)+16=?

n=3:
3(3)+16=?

etc etc :)

Answer 9

@alexray19 thank you so much that really made it a lot easier! :) When I solved the equations with the formula you gave me I got 64=16, 46=10, and 61=15. I know B is out of the picture because it was .00000 something, but which ones would be correct? Does it have to be just 16 which would make the answer 64 or do 46 and 61 fall on the line as well?

Answer 10

@DebbieG thank you for clarifying! :)

Answer 11

I'm a little confused by your post... lol. I think you have the correct answers, but lets make sure you understand the reasoning. :)

We are trying to see if a counting number n will give each of the results. If so, then that number IS a term in the sequence; if not, it isn't (because it falls between 2 terms in the sequence).

A. 64=3n+16
48=3n
n=16 which is an integer, so this is in the sequence, for n=16

B. 48 =3n+16
32=3n
n=32/3 not an integer, so this is not in the sequence (notice that for n=10 we get a_n=46, and for n=11 we get a_n=49)

C. 46 = 3n+16
30=3n
n=10, so in the sequence

D. 61=3n + 16
3n=45
n=15, so in the sequence

That's really all there is to it - just solve for n, and see if it's a positive integer. :)

Answer 12

Ohhh wait, does it say \[an=3n+16\]exactly? Like is the letter "a" a variable too?

Answer 13

It's a sequence, so I'm interpreting that as \(\Large a_{n}\).

Answer 14

@DebbieG thank you! that makes sense, i just get confused when I have to put it into equation form, I didnt know how to do that at all.. thank you! @alexray19 its supposed to be a sub n :)

Answer 15

You're welcome. :)