4 years ago

Correct and best explained answer gets brainliest.

2 answers:

5 0

2, 8, 32, 128, 512, 2048, and here's why:
The pattern is the number times 4.
1: 2
2: 2*4 is 8,
3: 8*4 is 32,
4: 32*4 is 128,
5: 128*4 is 512,
6: 512*4 is 2,048.

Add these together...
2 + 8 + 32 + 128 + 512 + 2,048 = 2,730

Your answer is "D)", 2,730.

nalin [4]4 years ago

3 0

Okay, so the pattern is multiplying by 4. so to find the next two numbers: 128 times 4=512 times 4=2048. so all six numbers are 2, 8, 32, 128, 512, and 2048. Add all six together and you get D-2730.

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Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.

Damm [24]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=-0.25\\ a_1=256\\ n=9 \end{cases}$

$\bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)} \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right) \\\\\\ S_9=256\left( \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125$