Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
9514 1404 393
Answer:
- common ratio: -2
- first term -3/4
- sum of 11 terms: -2049/4
Step-by-step explanation:
The formula for the generic term can be solved to find the first term and the common ratio.
an = a1·r^(n-1)
For the given terms, we have ...
a4 = 6 = a1·r^(4 -1)
a7 = -48 = a1·r^(7-1)
Dividing the second equation by the first gives ...
a7/a4 = -48/6 = r^(6 -3)
r = (-8)^(1/3)
r = -2 . . . . . . . . . . the common ratio
Then the first term is ...
6 = a1·(-2)^(3) = -8a1
-6/8 = a1 = -3/4 . . . . . the first term
__
The sum of N terms is ...
Sn = a1·(r^n -1)/(r -1)
Then the sum of 11 terms is ...
S11 = (-3/4)((-2)^11 -1)/(-2-1) = (-1/4)(2^11 +1)
S11 = -2049/4 . . . . . the sum of 11 terms
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.