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kicyunya [14]
3 years ago
15

Find the 100th AND the nth term for the following sequence. Please show work.

Mathematics
1 answer:
balandron [24]3 years ago
3 0

Answer:

nth term of this sequence is (197+(n+6)\times 3^{27})

and 100th term is (197+106\times 3^{27}).

Step-by-step explanation:

The given sequence is (197+7\times 3^{27}),(197+8\times 3^{27}),(197+9\times 3^{27})

Now we will find the difference between each successive term.

Second term - First term = (197+8\times 3^{27})-(197+7\times 3^{27})

                                         = (8\times 3^{27}-7\times 3^{27})

                                         = 3^{27}(8-7)

                                         = 3^{27}

Similarly third term - second term = 3^{27}

So there is a common difference of 3^{27}.

It is an arithmetic sequence for which the explicit formula will be

T_{n}=a + (n - 1)d

where T_{n} = nth term of the arithmetic sequence

where a = first term of the arithmetic sequence

n = number of term

d = common difference in each successive term

Now we plug in the values to get the 100th term of the sequence.

T_{n}=(197+7\times 3^{27})+(n-1)\times 3^{27}

               = (197+(n+6)\times 3^{27})

T_{100}=(197+7\times 3^{27})+(100-1)\times 3^{27}

                   = 197+7\times 3^{27}+99\times 3^{27}

                   = 197+106\times 3^{27}

Therefore, nth term of this sequence is (197+(n+6)\times 3^{27})

and 100th term is (197+106\times 3^{27}).

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==============================

Explanation:

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Angle 2 = angle 8 because they are vertical angles, same can be said for angle 1 and angle 7. Also, we know that angle 3 = angle 5, and angle 4 = angle 6.

Furthermore, the alternate interior angles are congruent so angle 8 = angle 4 and angle 7 = angle 3.

Based on all that we can fill out a lot of the angles. You'll have the same answers repeated over and over. The even numbered angles (angle 2, angle 4, angle 6, angle 8) are all 67 degrees. The odd numbered angles (angle 1, angle 3, angle 5, angle 7) are 113 degrees.

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A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33.
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Answer:

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be <em>x </em>and <em>y</em>, where <em>y</em> is the larger of the two numbers.

Since <em>y</em> is the larger number, it is one more than the smaller number. So:

y=x+1

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y = 4\sqrt{2} + 1 \approx6.66

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