Question

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

a19 = -92, a20 = 6

Answer 1

Just from these two numbers you can find your common difference, then work backwards to find term 1 and write the equation.

Answer 2

@MightyChondrion i am a little confused with what you said or how to go about this

Answer 3

In arithmetic sequences, we have this thing called the common difference. It's a number that tells us what we add to a term to get the next term. In this case, your CD is the number added to -92 to get 6, what is that number?

Answer 4

98

Answer 5

Yeah, that's right. Do you know the formula for finding the nth term of an arithmetic sequence?

Answer 6

no

Answer 7

These are the four choices I was given

an = -1856 + 98(n - 1)
an = -1856 - 98(n - 1)
an = -1856 - 98(n + 1)
an = -1856 + 98(n + 1)

Answer 8

\[u _{n}=u _{1}+(n-1)d\]
Where \[u _{n}\] is your nth term, in this case, you have term 19, and u\[_{1}\] is the first term you need to find. N is simply what number term you have (19) and d is your common difference aka the number added to a term to get the next term.

Answer 9

Now if you plug into this formula, you have \[u _{n}=-92\] so you can write that as \[-92=u _{1}+(19-1)*98\]. Solve for the first term now

Answer 10

-u1=1856

Answer 11

@MightyChondrium

Answer 12

Mhm, now you can represent the nth term as \[u _{n}=-1856+98(n-1)\]