Answer:
We think you wrote:
2,-16,128,-1024
This deals with geometric series.
Step-by-step explanation:
Step by Step Solution
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2,-16,128,-1024
Your input appears to be an geometric series.
Find the ratio (r) between adjacent members
a2/a1=-16/2=-8
a3/a2=128/-16=-8
a4/a3=-1024/128=-8
The ration (r) between every two adjacent members of the series is constant and equal to -8
General Form: a
n
=a
1
×r
n-1
This geometric series: a
n
=2×-8
n-1
The nature of this series
Sum of finite geometric series members
sum of a geometric series
The sum of our particular series
a 1-rn = 2 1--84 = 2 1-4096 = 2 -4095 =2×-455=-910
1-r 1--8 9 9
Finding the n
th
element
a2 =a1×r2-1 =a1×r1 =2×-81 =-16
a3 =a1×r3-1 =a1×r2 =2×-82 =128
a4 =a1×r4-1 =a1×r3 =2×-83 =-1024
a5 =a1×r5-1 =a1×r4 =2×-84 =8192
a6 =a1×r6-1 =a1×r5 =2×-85 =-65536
a7 =a1×r7-1 =a1×r6 =2×-86 =524288
a8 =a1×r8-1 =a1×r7 =2×-87 =-4194304
a9 =a1×r9-1 =a1×r8 =2×-88 =33554432
a10 =a1×r10-1 =a1×r9 =2×-89 =-268435456
a11 =a1×r11-1 =a1×r10 =2×-810 =2147483648
a12 =a1×r12-1 =a1×r11 =2×-811 =-17179869184
a13 =a1×r13-1 =a1×r12 =2×-812 =137438953472
a14 =a1×r14-1 =a1×r13 =2×-813 =-1099511627776
l hope it's help
