the number of even integers between 1 and 103 is the same is the same as the number of odd integers between 4 and x. what is the value of x?

# of numbers between 1 & 103: 102
Half of that would be even numbers. So, 51 even numbers.
Between 4 and x, there are 102 numbers. 4+102=106. 4+106=x. 106=x

Answer Link

aksnkj aksnkj · Answer 2 · 2021-10-03T19:29:34+02:00

Answer:

The value of [tex]x[/tex] is 106.

Step-by-step explanation:

You are given numbers between 1 and 103.

Now, the even integers between 1 and 103 will be 2, 4, 6, ......, 102.

The numbers form an AP (arithmetic progression) whose first term is [tex]a=1[/tex] and common difference is [tex]d=2[/tex]. Last term is [tex]a_n=103[/tex]

Now, the number of terms in 2, 4, 6, ......, 102 will be,

[tex]a_n=a+(n-1)d\\103=1+(n-1)2\\n=52[/tex]

So, according to the question, there will be 52 odd integers between 4 and [tex]x[/tex].

So, the value of [tex]x[/tex] will be, (using the same concept of AP as above)

[tex]x=4+(52-1)2\\x=106[/tex]

The value of [tex]x[/tex] is 106.

For more details, refer the link:

https://brainly.com/question/13989292?referrer=searchResults