Question

Find the 9th term of the arithmetic sequence.

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

Answer 1

know the n'th term formula ?

Answer 2

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

Answer 3

For Arithmetic sequences,
\(\huge a_n =a_1 +(n-1)d \)

Note it down,
a1 = 1st term
d = common difference
n = number of terms

Answer 4

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

Answer 5

a10 = 100

100 = a1 + 9d
got this ?

Answer 6

yeah

Answer 7

a20 = 50
can you make another equation ?

Answer 8

yeah
50=a1+19d

Answer 9

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

Answer 10

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

Answer 11

you never subtracted 2 equations ?

100-50 = a1- a1 + 9d -19d

Answer 12

simplify that

Answer 13

tried ?

Answer 14

50=-10d??

Answer 15

d=-5?

Answer 16

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

Answer 17

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

Answer 18

100 = a1+9d

100 = a1 - 45
....

Answer 19

a1=55

Answer 20

no...

Answer 21

145...

Answer 22

100 = a1-45

a1 = 100+45
yes

Answer 23

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

Answer 24

and you have already calculated a1 and d

Answer 25

105

Answer 26

\(\huge \checkmark \)

Answer 27

yay thank you!!!

Answer 28

welcome ^_^