Answer:
Explanation:
The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = (ar^n - 1)/(r - 1)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
1) 2 – 4 + 8 – 16 + ...
a = 2
r = - 4/2 = - 2
n = 6
Since r is negative, we would use
Sn = a(1 - r^n)/(1 - r)
Therefore, the sum of the first 6 terms, S6 is
S6 = 2(1 - (- 2^6))/(1 - - 2)
S6 = 2(1 - 64)/3 = (2 × - 63)/3
S6 = - 42
2) -2, 6, -18, 54
a = - 2
n = 4
r = 6/- 2 = - 3
S4 = - 2(1 - (- 3^4))/(1 - - 3)
S6 = - 2(1 - 81)/4 = (- 2 × - 80)/4
S6 = 40
3) 1, 2, 4, 8, 16, 32, 64, 128, 256
r = 2/1 = 2
n = 9
a = 1
Sn = (ar^n - 1)/(r - 1)
S9 = (1 × 2^9 - 1)/(2 - 1)
S9 = 512 - 1
S9 = 511