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If the 4th and 7th terms of a G.P are −1/2 and
− 4, respectively, then find G5 and S6 .​

Sagot :

abidemiokin

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

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