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

\[\huge\rm a_n=a_1 *r^{n-1}\]
general form equation for a geometric sequence
n=number of the term ( so to find first term n=1 for 2nd term n=2)
a_1 = first term
r=common ratio
given terms are fifth which is 567
and 2nd which is -21
so plug that in

Answer 2

like for 2nd term n=-21 i can replace n with 2
\[\large\rm a_\color{red}{n}=a_1 *r^{\color{ReD}{n}-1}\]
\[\large\rm a_\color{red}{2}=a_1 *r^{\color{ReD}{2}-1}\]
and since a_2 =-21 and i ca substitute that too
\[\large\rm \color{red}{-21}=a_1 *r^{\color{ReD}{1}}\]
^first equation)
now plugin fifth term
and then divide them (it's geometric sequence so we should divide both equation )

Answer 3

567 = a_1 * r^5-1

567 = a_1 * r^4