Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -8 and 512, respectively.

Answer 1

know the general formula for n'th term ?

Answer 2

the initial number with the pattern and (n-1)

Answer 3

not sure how to do it with the 2nd and 5th term though

Answer 4

\(\Large a_n = a_1 r^{n-1}\)

Answer 5

a1 is the 1st term
an is the n'th term
r is the common ratio

Answer 6

2n term is -8

this just means
that when

n=2, a2 = -8

Answer 7

so we get
\(-8 = a_1 (2)^{n-1}\)
do u get this ?

Answer 8

ar^(n-1)=t_n. hence ar=-8 and ar^4=512 solve for r

Answer 9

after getting the value of r, puting in ar=-8 and get the value of a, once you get the value of a, just put the values of r and a in ar^(n-1)

Answer 10

@faariat

Answer 11

Check the attachment please

Answer 12

im kind of confused

Answer 13

which part??

Answer 14

im not really sure what was done in the attachment

Answer 15

Ok you know the formula of the nth term of a GP? @faariat

Answer 16

no

Answer 17

It is a*r^(n-1) '^' means raised to the power. a is the first term of the sequence and r is the common ratio

Answer 18

ok so how do i use this with the numbers given to me?

Answer 19

so your aim is to find a and r right ?? to get the nth term??

Answer 20

yes

Answer 21

we are given the second and fifth term right?

Answer 22

yes so how do we use those?

Answer 23

now check me attachment again.

Answer 24

oh wow that makes so much more sense now thank you!!!!!

Answer 25

is it clear now completely? I hope you can solve this kind of problems now.:)