Find the 53rd term of the arithmetic sequence -12, -1, 10

Mathematics

2 answers:

RSB [31]2 years ago

5 0

440 is the answer

Tn=a+(n-1)d

Tn=53

a= -12

n=53

d= 11

-12+(53-1)11 = 440

fgiga [73]2 years ago

3 0

Answer:

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

Since we're finding the 53rd term

a = - 12

n = 53

d = -1 - ( -12) = - 1 + 12 = 11 or 10--1 = 10 +1 =11

d = 11

So we have

A(53) = - 12 + (11)(53 - 1)

= - 12 + 11(52)

= -12 + 572

= 560

We have the final answer as

Hope this helps you

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Use interval notation to express the set of real numbers x that satisfies the inequality (x+2)(x-5) < 0.

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The interval notation to express the set of real numbers <u>x</u> that satisfies the given inequality is -2<x<5. You also can represent it as (-2,5)

<h3>Inequality</h3>

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for the given inequality.

First, you should find the critical points of the inequality.

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x = -2

and

x-5=0

x=5

Write, the intervals in between critical points. Therefore, -2<x<5.

Read more about inequalities here.

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