Find $a_1$ and d for for an arithmetic sequence with these terms:

$a_3 = -8$ and $a_7 = 32$

Question

Find $a_1$ and d for for an arithmetic sequence with these terms:

$a_3 = -8$ and $a_7 = 32$

igreen · Answer

@hartnn @ganeshie8

igreen · Answer

@phi

igreen · Answer

..

igreen · Answer

How did you get that?

anonymous · Answer

1sec

igreen · Answer

Find the three arithmetic means in this sequence.

2, __, __, __, -18

igreen · Answer

Do you know this? @kirbykirby

kirbykirby · Answer

$a_n=a_m+(n-m)d$
where
$a_7=a_n$ and $a_3=a_m$

igreen · Answer

So what am I supposed to do with that..?

kirbykirby · Answer

you can compare the indices, and see that $n = 7$ and $m=3$
now you can plug in those values into the formula
$32 = -8(7-3)d$

igreen · Answer

Oh..

igreen · Answer

$32 = -8(7 - 3)d$
$32 = -56d + 24d$

Is that right..?

kirbykirby · Answer

yes

igreen · Answer

$32 = -32d$
$d = -1$

kirbykirby · Answer

oh wait I forgot the + when I re-wrote it with numbers.. sorry:
$32 = -8\color{red}{+}(7-3)d$

igreen · Answer

$32 = -8 + 7d - 3d$
$32 = -8 + 4d$
$40 = 4$
$d = 10$

igreen · Answer

*4d

kirbykirby · Answer

yes that is good :) sorry again..

igreen · Answer

Lol, fine. I have a few more..I'll tag you. :)

kirbykirby · Answer

so finding $a_1$ will be the same as above:
$\large a_{\color{red}{3}} = a_\color{blue}{1}+(\color{red}{3}-\color{blue}{1})(10)$