Question

@mathmale

Answer 1

What is the first term of the given sequence?

What is the common difference, from one term to the next? Are we going UP or DOWN?

Answer 2

The common difference seems to be -3 and the first term is 11

Answer 3

Great. That's correct. Let the first term be "a" and the common difference "d".

Subst. these values into this formula: l = a + (n-1) d

where " l " is the nth term and could also be represented by \[a _{1}\]

Answer 4

l = 11 + (n-1) -3

Answer 5

Have to enclose that -3 inside parentheses, because of its being negative. Do that, please?

Answer 6

l = 11 + (n-1-3)?

Answer 7

l = 11 + (n-1)(-3). Again, the reason for this is that -3 is negative, and you want to show multiplication by (-3), not subtraction of 3 (as in -3).

Answer 8

Now multiply (n-1) by -3. Your result?

Answer 9

3n-3

Answer 10

Good start, but not quite right. (-3)(n-1) = -3n + 3.

You had l = 11 + (n-1)(-3).

Re-write this, replacing that (n-1)(-3) with -3n +3.

Answer 11

Would the answer be option B?

a1=11, an=an-1 -3? @mathmale

Answer 12

"replacing that (n-1)(-3) with -3n +3" would give you l = 11 + 3 - 3n. Could you simplify this?

Answer 13

You could add 11 and 3 together and get 4-3n

Answer 14

If you are using subscripts such as n and n-1, it's important to actually write them as subscripts:

\[a _{n},~ a _{n-1}\]

Answer 15

Otherwise there's room for confusion about what your n-1 represents.

Answer 16

Okay, but when you asked if I could simplify I got 4-3n

Answer 17

Would the answer be B?

Answer 18

@mathmale

Answer 19

Sorry for the delay. You've been correct all along in stating that the first term is 11.

That rules out the last 2 answers.

Would you mind focusing on the first 2 answers and deciding which one is correct?

I would suggest you use the first answer to predict 8, 5, 2, etc. does it do so correctly?

If not, use the 2nd answer to predict 8, 5, 2, etc. does it "work"?

Answer 20

So, plug in the numbers or something like that?

Answer 21

Can you help me with that, please?

Answer 22

Yes. supposing that the first equation is \[a _{n}=a _{n-1}-4\]

Answer 23

if n=1, then a_sub_1 is 11.
If n=2, then you have\[a _{2}=a _{2-1}-4, or \]

Answer 24

\[a _{2}=11-4\]

Answer 25

Did this correctly produce 8?

If not, then the first equation is wrong, leaving you with the second equation as right.

I have to get off the 'Net, but would be happy to help you further later on.

Answer 26

Wait, so option B is correct?