yoda82
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Ask your questions and receive precise answers from experienced professionals across different disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.