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Paul [167]
3 years ago
14

What is the nth term?

Mathematics
1 answer:
kumpel [21]3 years ago
7 0

Let a_k denote the <em>k</em>th term of the sequence. Then

a_k=a_1+d(k-1)

where <em>d</em> is the common difference between consecutive terms in the sequence and <em>a</em>₁ is the first term.

The sum of the first <em>n</em> terms is

S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n

From the formula for a_k, we get

S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)

S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k

S_n=na_1+\dfrac{d(n-1)n}2

S_n=\dfrac n2(2a_1-d+dn)

So we have d=-5, and 2a_1-d=16 so that a_1=\frac{11}2.

Then the <em>n</em>th term in the sequence is

a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}

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Answer:

x=10, y = -20

Step-by-step explanation:

y = –5x + 30

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3 years ago
Daily low temperatures in Columbus, OH in January 2014 were approximately normally distributed with a mean of 15.45 and a standa
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Answer: 12.10

Step-by-step explanation:

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The formula to calculate the z-score :-

z=\dfrac{x-\mu}{\sigma}

For x= 5 degrees

z=\dfrac{5-15.45}{13.70}=-0.7627737226\approx-0.76

For x= 10 degrees

z=\dfrac{10-15.45}{13.70}=-0.397810218\approx-0.40

The P-value : P(-0.76

=0.3445783-0.2236273=0.120951\approx0.1210

In percent , 0.1210\times100=12.10\%

Hence, the percentage of days had a low temperature between 5 degrees and 10 degrees = 12.10%

5 0
3 years ago
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Step-by-step explanation:

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It should have 2 solutions
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Add 11p to both sides.

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3 years ago
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