Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Answer 1

ok... so its geometric

that means the 2th term is

\[-21 = ar^{2-1}... or.... -21 = ar^1\]

you will need to substitute this equation into the equation for the 5th term

and you also know the 5th term

\[567 = ar^{5-1}... or... 567 = ar^4\]

this can be rewritten as

\[567 = ar^1 \times r^3\]

if you subsitute you be able to find the value of r, the common ratio

from there you will be able to find the 1st term

and hence the general term

hope this makes sense

Answer 2

okay so it would be an = 7 • (-3)n + 1

Answer 3

and the general term in a geometric series is

\[a_{n} = ar^{n -1}\]

Answer 4

so this an = 7 • 3n - 1

Answer 5

yep, that seems better

Answer 6

or do i keep the brackets on 3

Answer 7

an = 7 • (-3)n - 1

Answer 8

yes in brackets

\[A_{n} = 7 \times (-3)^{n -1}\]

Answer 9

thank you!!