9514 1404 393
Answer:
- common ratio: -2
- first term -3/4
- sum of 11 terms: -2049/4
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