Question

Im stuck on a lot of questions, here they are:

24 + 12 + 6 + ...(S7)
Sn = 24(2^7-1)/2-1
S7 = 24(127)/1
S7 = 3048/1

Thats what I got as an answer, but it's wrong, the real answer is a fraction answer, and its 381/8. How did they get that???

The other one was:

512 + (-256) + 128 +... +(-1)
Sn = -2(-1)-512/-2-1
= -510/-3

This answer is somehow wrong too:/

And the other one:

-8 -2 -1/2...-1/128

Sn = 4(-1/128)-8/4-1
Sn = 4/1 * 128/1 = 512 *-8
Sn = -4096/3
= This is also the wrong answer. Im soo confused ://// It's supposed to be 1356/128

Answer 1

1st:
your r value is 1/2, you used it as +2
Sum(7) = 24((1/2)^7 - 1)/(1/2-1)
= 24(1/128 - 1)/(-1/2)
= 24(-127/128)(-2) = 381/8

2nd:
a = 512 , r = -1/2
first find number of terms, last term is -1
t(n) = ar^(n-1)
-1 = 512(-1/2)^(n-1)
-1/512 = (-1/2)^(n-1)
(-1/2)^9 = (-1/2)^(n-1)
9 = n-1
n = 10

so Sum(10) = 512((-1/2)^10 - 1)/(-1/2-1)
= 512(-513/512)(-2/3)
= 342

3rd:

-8 - 2 - 1/2 - ... - 1/128
a = -8 , r = 1/4 , n = ??
term(n) = ar^(n-1)
-1/128 = -8(1/4)^(n-1)
1/1024 = (1/4)^n-1
(1/4)^5 = (1/4)^(n-1)
5 = n-1
n = 6
the series is
-8 -2 -1/2 -1/8 -1/32 - 1/128

sum(6) = -8((1/4)^6 - 1)/(1/4 -1)
= -8(-4095/4096)/(-3/4)
= -8(-4095/4096)(-4/3)
= -1365/128