Question

arithmetic sequence: A5=11, A11=29

Answer 1

So I know there are formulas and stuff to figure this out but I never remember them. I think what you do is figure out how many more steps you need between the two terms, then subtract the two terms and divide by the number of steps needed. This both makes sure you arrive at 29 and you have even spacing on the way there.

Answer 2

I know the formula is An= d(n-1) +A1

Answer 3

A5= a+4d+=11
A11=a+10d=29
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-6d=-18

Answer 4

That doesn't really makes sense lol...

Answer 5

Figure this one out yet? :)

Answer 6

No, not yet.. I was thinking like A5=d(5-1)+A11..

Answer 7

In an arithmetic sequence,
there is some `common difference` between each term.

We usually denote it as \(\rm d\) as you have shown.
So to get from one term to the next, we add \(\rm d\).
To get from A5 to A6, we +d.
To get from A6 to A7, we +d again, so that's +2d from A5 to A7.

So get from A5 to A11, we'll have to add 6 of those d's.
So our 11th term is actually the 5th term plus 6 of those d's.

\(\rm A_{11}=A_5+6d\)

Answer 8

Plugging in our values,\[\rm 29=11+6d\]allows us to solve for this common difference \(\rm d\).

Answer 9

So 3?

Answer 10

Its says here that I have to fine the nth term.. And my answer is An= -4+3n , idk how to get there tho.

Answer 11

Ok so we've finished the first part, finding our common difference: \(\rm d=3\).

To get from A1 to A2 we add d, \(\rm A_2=A_1+d\)
To get from A1 to A3 we add d twice, \(\rm A_3=A_1+2d\)
Here is another clever way we can write that, \(\rm A_3=A_1+(3-1)d\)

We're always adding one less d than the number of the term we're on.
This should make sense since we don't add any d to get A1.

So good, that establishes our general formula,
to get from the first term to the nth term, we'll add n-1 d's.
\(\rm A_n=A_1+(n-1)d\)

To get from A1 to A5, we add 4 of those d's,
\(\rm A_5=A_1+4d\)

Answer 12

We're doing this because we another piece for our general form, the first term A1.

Answer 13

So plug in the information that you know,
and solve for A1.

Answer 14

This type of problem is `three steps`:

1. Find your common difference \(\rm \color{orangered}{d}\).
2. Find your first term \(\rm \color{royalblue}{A_1}\).
3. Plug that information into the general formula \(\rm A_n=\color{royalblue}{A_1}+(n-1)\color{orangered}{d}\).