Question

Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164

Answer 1

The nth term of an arithmetic sequence is:
\(\Large a_n = a_1 + (n-1)d\)

Answer 2

the formula is an=a1+(n-1)d

Answer 3

How do I find a1 though? and would the common difference be -3?

Answer 4

Put n = 19 in the above equation.
Then put n = 21.
Solve the two equations to find \(a_1\) and d.

Answer 5

is this module 8?

Answer 6

How do you set that up????

Answer 7

\(\Large a_n = a_1 + (n-1)d\)
put n = 19
\(\Large a_{19} = a_1 + (19-1)d = -58\)
\(\Large a_{19} = a_1 + 18d = -58\)

Try the same with n = 21

Answer 8

so I end up with a19=a1 + 18d = -58 and a21 + 20d = -64
now what?

Answer 9

a21 = a1 + 20d + -64*

Answer 10

= -64

Answer 11

a1 + 18d = -58
a1 + 20d = -164 (-164 not -64 and RHS is a1 not a21)
Subtract first from second:
2d = -164 + 58 = -106
d = -106/2 = -53

a1 + 18d = -58
a1 + 18(-53) = -58
a1 - 954 = -58
a1 = 954 - 58 = 896

So the nth term is:
\(\Large a_n = 896 -58(n-1)\)

Answer 12

Sorry. The nth term is: \(\Large a_n = 896 -53(n-1)\)

Answer 13

Thank you so much I totally understand now!!

Answer 14

You are welcome.