The answer is: " 23 " .
→ The fourth number in the sequence is: " 23 " .
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Explanation:
To solve:
" x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;
in which:
"x" = The first number in these sequence;
"(x + 1 )" = the second number in the sequence;
"(x + 2)" = the third number in the sequence;
"(x + 3)" = the fourth number in the sequence;
"(x + 4)" = the fifth number in the sequence;
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Solve for the "fourth number in the sequence" ; or: "(x + 3)" ;
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Given: " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;
↔ " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;
→ Solve for "x" ;
→ then, solve for "(x + 3)" ;
→ which is the fourth number in this sequence;
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→ " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;
"5x + 1 + 2 + 3 + 4= 110 " ;
" 5x + 10 = 110 " ;
Solve for "x" :
Subtract "10" from EACH SIDE of the equation; as follows:
" 5x + 10 - 10 = 110 - 10 " ;
to get :
" 5x = 100 " ;
Now, divide EACH SIDE of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ; as follows:
5x / 5 = 100 / 5 ;
to get:
" x = 20 " .
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Now, to find the fourth number in the sequence:
→ " (x + 3) " ;
→ Substitute "20" for "x" ;
" x + 3 = 20 + 3 = 23" ;
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The answer is: " 23 " .
The fourth number in the sequence is: " 23 " .
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Let us check our work:
If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then: "24" is the "fifth number" .
As such: "22" is the "third number" ; "21" is the "second number" ; and "20" is the "first number" . Is this consistent with: "x = 20" as the "first number" ? Yes!
Thus, "20 + 21 + 22 + 23 + 25 = ? 110 ? ? ;
→ 20 + 21 = 41 ;
→ 41 + 22 = 63 ;
→ 63 + 23 = 86 ;
→ 86 + 24 = 110 . Yes!
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Hope this answer is helpful!
Best wishes in your academic pursuits—
and within the "Brainly" community!
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