Answer:
the 7th term of the geometric sequence is 1/4 or 0.25
Step-by-step explanation:
Given geometric sequence terms
a1 = 1,024 and a4 = −16
nth term of geometric sequence is
\(a_n= a_1(r)^{n-1}\)
a1 = 1,024 and a4 = −16
Plug in 4 for n and solve for 'r'
\(a_4= a_1(r)^{4-1}\)
\(-16= 1024(r)^{3}\)
Divide both sides by 1024
\(\frac{-1}{64} = r^3\)
Now take cube root on both sides
\(\frac{-1}{4} = r\)
To find 7th term we plug in n=7 , r= -1/4 , a1 = 1024
\(a_n= a_1(r)^{n-1}\)
\(a_7= 1024(-1/4)^{7-1}\)
\(a_7= 1024(-1/4)^{6}\)
a_7 = 0.25
