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Svetach [21]
3 years ago
13

Solve the inequality and graph the solution set on a number line. Express the solution set in both​ set-builder and interval not

ations.
-8 < x -3 < 1
Mathematics
1 answer:
shusha [124]3 years ago
8 0
<span>-8 < x -3 < 1
we have two inequations: 
* -8<x-3 and -8+3<x-3+3 or -5 < x or x>-5
*  x-3<1 or x-3+3<1+3 and we have x<4
For all cases we have -5<x<4
or </span><span>interval notations: x</span>∈(-5;4)
have fun
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An arithmetic sequence has t1=5 and t2=8 find tn and sn
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a_n=2+3n

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

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<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

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an = nth term

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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

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Operating:

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