Question

What is the 7th term of the geometric sequence where a1 = –4 and a5 = –1,024?

Answer 1

Answer:

16384

Step-by-step explanation:

The common ratio  r  of this geometric sequence is a  4

th root of -

= -1024/-4 = 256 = 4∧4

Since  a5 = r4a1, The possible real  4th roots are =  ±4

Therefore, a7 = r²a5 = 16.(-1024)

= -16384

Thus the 7th term a7 can possibly be  16384

The Complex numbers  ±4i  are also  4th roots of  256,

if r = ±4i  then r² = -16 and

a7 = r²a5  = (-16)(-1024)

= 16384

Thus, the 7th term of the geometric sequence will be 16384.