Question

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

a19 = -58, a21 = -164
step by step please

Answer 1

one way is to develop a system of equations ....

Answer 2

\[a_o+d(19-1)=-58\\
a_o+d(21-1)=-164\]

Answer 3

might be a1 in in that case ....

Answer 4

a + 18d = -58
a + 20d = -164

-a - 18d = 58
a + 20d = -164
---------------
(20-18)d = (58-164)

d = (58-164)/(20-18)

Answer 5

so its
a + 18d = -58
a + 20d = -164

-a - 18d = 58
a + 20d = -164
---------------
(2)d = (-106)

d = (-106)/(2)
d=-53?

Answer 6

@amistre64 hey i'm still lost as in what to do next

Answer 7

you found the value for d, use it to find a; then all the parts will be accounted for

Answer 8

a + 18d = -58

a =-58- 18d

Answer 9

im assuming you know the general form of an arithmetic sequence to start with

Answer 10

i really don't , this is a new lesson for me and i'm struggling to understand.
a=-58-18(-53)
a=-58-(-954)
a=-58+954=896

Answer 11

the general form of defining the nth term of an arithmetic sequence is:\[a_1+d(n-1)\]
hence the need to define the a and d parts

Answer 12

we are given two solutions; which we can then create 2 equations with 2 unknowns with; which is what we started out doing; then we determine their values

Answer 13

test it out;

does: 896 - 53(19-1) = -58 ?

does: 896 - 53(20-1) = -164 ?

Answer 14

if so; then:\[a_n=896-53(n-1)\]

Answer 15

21-1 that is; fingers got a little ahead

Answer 16

896-53(18)=896-954=-58
896-53(20)=896-1060=-164
ok it makes sense now thank you

Answer 17

youre welcome