Answer:
G5 = -1
S6 = -63/16
Step-by-step explanation:
The formula for finding the nth term of a GP is Tn = ar^n-1
a is the first term
r is the common ratio
n is the number of terms
If the 4th term is -1/2
T4 = ar^4-1
T4 = ar³ = -1/2.... 1
If the 7th term is -4
T7 = ar^7-1
T7 = ar^6 = -4.... 2
Divide both equation
ar^6/ar³ = -4/(-1/2)
r³ = -4×-2
r³ = 8
r = 2
Common ratio is 2
Since ar³ = -1/2
a(2)³ = -1/2
8a = -1/2
a = -1/16
The first term is -1/16
Get the fifth term G5
G5 = ar⁴
G5 = (-1/16)(2)⁴
G5 = (-1/16)(16)
G5 = -1
Get the sum of the first six terms S6
S6 = a(r^n-1)/r-1
S6 = -1/16(2^6-1)/2-1
S6 = -1/16(64-1)
S6 = -63/16
Hence the sum of the first six terms is -63/16
