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Anna007 [38]
2 years ago
9

An arithmetic sequence has t1=5 and t2=8 find tn and sn

Mathematics
1 answer:
RoseWind [281]2 years ago
4 0

Answer:

a_n=2+3n

\displaystyle S_n=\frac{7n+3n^2}{2}

Step-by-step explanation:

<u>Arithmetic Sequences </u>

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

a_n=a_1+(n-1)r

Where

an = nth term

a1 = first term

r   = common difference

n  = number of the term

The sum of the n terms of an arithmetic sequence is given by:

\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n

We are given the first two terms of the sequence:

a1=5, a2=8. The common difference is:

r = 8 - 5 = 3

Thus the general term of the sequence is:

a_n=5+(n-1)3=5+3n-3=2+3n

\boxed{a_n=2+3n}

The formula for the sum is:

\displaystyle S_n=\frac{5+2+3n}{2}\cdot n

\displaystyle S_n=\frac{7+3n}{2}\cdot n

Operating:

\boxed{\displaystyle S_n=\frac{7n+3n^2}{2}}

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Step-by-step explanation:

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Answer:

B: y = -2x + 5

Step-by-step explanation:

-2 - 1 = -3

9 - 3 = 6

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gradient = -2

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equation = y = -2x + 5

so the answer is option b

7 0
3 years ago
The sum of three consecutive odd integers is 195. Find the three integers.
Anettt [7]
Good afternoon, 

x= first odd integer 
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x+4= third intenger

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x + (x+2) + (x+4) = 195
3x = 195 - 4 - 2
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8 0
3 years ago
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A random sample of individuals over the age of 18 are sampled and asked, "What is your level of education?" The results are summ
grigory [225]

Answer:

Check the explanation

Step-by-step explanation:

1.  The level of education as high school diploma (31% area).

Therefore the most frequent education level is High school Diploma.

2. Suppose there are 200 people in random sample. Pie diagram shows the percentage of people with Bachelor's degree is 19%

Therefore the number of people having Bachelor's degree among 200 people = 200×19% = 38

Therefore the answer is 38 .

3. Now the population size given is 6000. The percentage of individuals who have some collage but no degree is 17%

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Thereforethe answer is 1020 .

4. The percentage of individuals who have an associate's degree is 9% as per the pie diagram. The above pie diagram is based on a random sample of individuals. If we take another sample then also we may get different result. Therefore if we considere the entire population of U.S.A. the percentage of individuals who have an associate's degree may differ from 9% .

4 0
2 years ago
<img src="https://tex.z-dn.net/?f=%5Csqrt%5B-%5D%7B64%7D" id="TexFormula1" title="\sqrt[-]{64}" alt="\sqrt[-]{64}" align="absmid
Gemiola [76]
Answer: -8





Explanation:

-sqrt(64)

If 8 x 8 = 64, then the square root of 64 is 8.

Result: -8

3 0
3 years ago
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