Question

Find an equation for the nth term of the arithmetic sequence.

a19 = -58, a21 = -164

Answer 1

@Nnesha

Answer 2

hey:=)
we need common difference and first term to write an equation
arithmetic equation \[\huge\rm a_n = a_1 + (n-1)d\]

where a_1 = first term
d=common difference
n= term that we have to find

Answer 3

given terms are a_{19}= -58 a_{21} = -164
plug this into the equation \[\large\rm a_\color{ReD}{{19}}=a_1 +(\color{ReD}{19}-1)d\]
19th term so we substitute n for 19
and a_{19} equal to -58 we can replace a_{19} with -58
\[\large\rm -58=a_1 +(\color{ReD}{19}-1)d\]
same for a_{21} write an equation when n =21

Answer 4

your turn:=) write an equation when n =21
just like i did for n=19 :=)

Answer 5

make sense ??

Answer 6

lets see, -164 = a1 (21 - 1)d ?

Answer 7

perfect!
\[\huge\rm -164 = a_1 +(\color{Red}{21-1})d\]
solve parentheses \[\large\rm -164 = a_1 +(\color{Red}{20})d\]
this is our 2nd equation
first one is \[\huge\rm -58 = a_1 +(\color{Red}{19-1})d\]
\[\large\rm -58 = a_1 +(\color{Red}{18})d\]

Answer 8

\[\large\rm -58 = a_1 + \color{Red}{18} d\]\[\large\rm -164 = a_1 + \color{Red}{20} d\]
we will use elimination method to solve this equation :=)
so subtract equation one from equation 2