Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively.

an = 3 • (-4)n + 1

an = 3 • 4n - 1

an = 3 • (-4)n - 1

an = 3 • 4n

Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively. 

 an = 3 • (-4)n + 1 

 an = 3 • 4n - 1 

 an = 3 • (-4)n - 1 

 an = 3 • 4n

anonymous · Answer

@RadEn

campbell_st · Answer

ok... so the basic formula for a term in a geometric sequence is 

$$a_{n} = ar^{n -1}$$

here is what you know 

2nd term 

$$-12 = a r^{2 -1} ...or...... -12 = ar$$

the 5th term 

$$768 = a r^{5 -1} ....or...... 768 = ar^4$$

this can be written using the 2nd term 

$$768 = ar \times r^3$$

substitute the value of the 2nd term 

$$768 = -12 \times r^3$$

you can now solve for r.... 

when you get r, 

substitute it into the 2nd term to find a.

then just substitute r and a into the general formula above

to get your answer. 

hope it helps