Given the sequence: 25, 21, 17, 13,... Write the explicit equation that models the sequence.
1 answer:
Answer:
The explicit equation that models the sequence is .
Step-by-step explanation:
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference.
In general, this is the standard explicit formula of an arithmetic sequence whose first term is A and common difference is B:
The sequence {25, 21, 17, 13, ...} is an example of an arithmetic sequence the same number, -4, is subtracted to each term to get to the next term.
We know the first term is 25 and common difference is -4.
Applying the standard explicit formula of an arithmetic sequence we get that
.
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9514 1404 393
Answer:
C. Obtuse
Step-by-step explanation:
The "form factor" I use for this is ...
a^2 + b^2 - c^2 = 6^2 + 8^2 - 11^2 = 36 +64 -121 = -21
The value is negative, indicating an OBTUSE triangle.
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<em>Additional comment</em>
In this expression, 'a' and 'b' are the two shortest sides (in no particular order) and 'c' is the longest side. The interpretation is ...
negative — obtuse
zero — right
positive — acute
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If you're familiar with Pythagorean triples, you know that the 3-4-5 right triangle triple can be doubled to give 6-8-10. The long side of 11 is longer than the hypotenuse for the right triangle, so would correspond to a largest angle greater than 90°. The 6-8-11 triangle would be OBTUSE.
