Find the 9th term of the arithmetic sequence.

a10 = 100 and a20 = 50; a9 = _____.

Question

Find the 9th term of the arithmetic sequence.

a10 = 100 and a20 = 50; a9 = _____.

hartnn · Answer

know the n'th term formula ?

anonymous · Answer

no, i just know find the differece and go with it. I work it out by hand it takes forever. But in this case I can't do that

hartnn · Answer

For Arithmetic sequences, 
$\huge a_n =a_1 +(n-1)d $

Note it down, 
a1 = 1st term
d = common difference 
n = number of terms

anonymous · Answer

but I don't know the common distance in this problem... That's why I posted it lol

hartnn · Answer

a10 = 100 

100 = a1 + 9d 
got this ?

anonymous · Answer

yeah

hartnn · Answer

a20 = 50
can you make another equation ?

anonymous · Answer

yeah 
50=a1+19d

hartnn · Answer

100 = a1 + 9d 
50  = a1 +19d
2 equations, 2 unknowns
Subtract them,and,
you will get the d

anonymous · Answer

How do I subtract them if they arent equal...

hartnn · Answer

you never subtracted 2 equations ? 

100-50 = a1- a1 + 9d -19d

hartnn · Answer

simplify that

hartnn · Answer

tried ?

anonymous · Answer

50=-10d??

anonymous · Answer

d=-5?

hartnn · Answer

correct!
now use any one of the equation to get a1

anonymous · Answer

so my equation would be 100=a1-5??
a1=95??

hartnn · Answer

100 = a1+9d

100 = a1 - 45
....

anonymous · Answer

a1=55

hartnn · Answer

no...

anonymous · Answer

145...

hartnn · Answer

100 = a1-45

a1 = 100+45
yes

hartnn · Answer

now we need, a9, so we plug in n=9 in
$\huge a_n =a_1 +(n-1)d$

hartnn · Answer

and you have already calculated a1 and d

anonymous · Answer

105

hartnn · Answer

$\huge \checkmark $

anonymous · Answer

yay thank you!!!

hartnn · Answer

welcome ^_^