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altavistard
Represent these consecutive numbers (assuming that they are all integers):

x
x+1
x+2
x+3
x+4
x+5
and so on
x+8
x+9 is the tenth number.  x+9 = 10, so x = 9.

Think of it this way:  there are 10 consecutive numbers, and the last one is 10.

Working backwards, we get the sequence 10, 9, ... 3, 2, 1.

The sum of such an arith sequence is equal to the count of the numbers times the average of the first and last terms:

sum here = 10(1+10)/2 = 5(11) = 55          (answer)

The sum of the number is 55.

Sequence and series

The sequence is a list of objects which have been ordered in a sequential manner, such that each member either becomes before or after. A series is a sum of sequence terms.

Given

10th of the 10 consecutive numbers is 10.

To find

The sum of all these numbers.

How do find the sum of these numbers?

We know the last number is 10.

let the first number be x

then tenth number will be x + 9

Then equate the tenth term

x + 9 = 10

     x = 10 - 9

     x = 1

Then the other number are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Then the sum is given by

[tex]\rm Sum = \dfrac{(n)(n+1)}{2}[/tex]

Here n is the last number

[tex]\rm Sum = \dfrac{(n)(n+1)}{2}\\\\\rm Sum = \dfrac{(10)(10+1)}{2}\\\\\rm Sum = \dfrac{10*11}{2}\\\\\rm Sum = \dfrac{110}{2}\\\\\rm Sum = 55[/tex]

Thus the sum of the number is 55.

More about the sequence and the series link is given below.

https://brainly.com/question/8195467

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