Question

Help? I cant figure out the correct answer

Find an equation for the nth term of the arithmetic sequence.
a_19 = -58, a_21 = -164

Answer 1

and these are the options:
an = 896 - 53(n - 2)
an = 896 - 53(n - 1)
an = 896 + 53(n + 1)
an = 896 - 53(n + 1)

Answer 2

a_19 means 19 th term and so on

Answer 3

but n th term is =a+(n-1)d where a is first term and d is common diff.

Answer 4

Walk yourself through it.

\(a_{1} = a\)
\(a_{2} = a + d\)
\(a_{3} = a + d + d = a + 2d\)
\(a_{4} = a + 3d = a + (4-1)d\)
\(a_{5} = a + 4d = a + (5-1)d\)
...
\(a_{n} = a + (n-1)d\)
...
\(a_{19} = a + (19-1)d = a + 18d = -58\)
\(a_{20} = a + (20-1)d = a + 19d\)
\(a_{21} = a + (21-1)d = a + 20d = -164\)

That is enough information to find 'a' and 'd'.