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

Question

campbell_st · Answer

well a term in a geometric series can be found using

$$a_{n} = a_{1} \times r^{n -1}$$

so you need to find the 1st term and the common ratio

using the information for the 5th term.... n = 2 you get 

$$-21 = a^{1} \times r^1$$

now the 5th term 

$$567 = a_{1} \times r^{4}$$

rewrite the 5th term to find r

$$567 = a_{1} \times r \times r^3$$

now substitute the 2nd term 

$$567 = -21 \times r^3$$

now you can solve for the common ratio r... 

and then solve for a1, the 1st term

hope it makes sense