Answer:
Step-by-step explanation:
Find the value of x. Part 1c
2 answers:
Answer: x = 11
<u>Step-by-step explanation:</u>
a) bottom triangle, bottom right angle: Using Linear Pair Postulate, 180° - 114° = 66°
b) bottom triangle, top angle: Congruent sides implies congruent angles = 66°
c) bottom triangle, bottom left angle: Using the Triangle Sum Theorem, 66° + 66° + y = 180° --> y = 48°
d) top triangle, bottom angle: Using Complimentary Angles Theorem, 90° - 48° = 42°
Congruent sides implies congruent angles:
42° = ∠2
42 = 2x + 20
22 = 2x
11 = x
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Answer:
31
Step-by-step explanation:
The series are given as geometric series because these terms have common ratio and not common difference.
Our common ratio is 2 because:
1*2 = 2
2*2 = 4
The summation formula for geometric series (r ≠ 1) is:
or
You may use either one of these formulas but I’ll use the first formula.
We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.
Therefore, the solution is 31.
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Summary
If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.
Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:
Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:
Above should be applied for series that have common ratio not equal to 1.
Above should be applied for series that have common ratio exactly equal to 1.
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Topics
Sequence & Series — Geometric Series
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Others
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