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marysya [2.9K]
3 years ago
12

Write the explicit formula that represents the geometric sequence-2, 8, -32, 128

Mathematics
1 answer:
maks197457 [2]3 years ago
4 0
Well,  since we know is a geometric sequence, we can always get the common ratio  of it by simply dividing one value by the one behind it... so let's do so, with say hmm -32 and 8  -32/8 = -4  <-- our common ratio

the first term is -2

\bf n^{th}\textit{ term of a geometric sequence}\\\\&#10;a_n=a_1\cdot r^{n-1}\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;r=\textit{common ratio}\\&#10;----------\\&#10;a_1=-2\\&#10;r=-4&#10;\end{cases}\implies a_n=-2(-4)^{n-1}
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Twice the sum of consecutive numbers n and n + 1 is 510. What is the smaller number?
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Answer:

The smaller number is 127

Step-by-step explanation:

Lets write the given problem in equation form

sum of consecutive numbers n and n + 1 = n + n + 1 = 2n + 1

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twice the sum of consecutive numbers n and n + 1 is 510

thus,

4n + 2 = 510

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