The largest of these 23 integers of an arithmetic progression is 112.
What is an arithmetic progression?
An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
The sum of 23 consecutive integers is 2323.
The integers are consecutive integers, so d = 1.
Number of terms, n = 23
The formula of sum of n terms is
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]2323=\frac{23}{2}[2a+(23-1)1][/tex]
⇒ [tex]2323(2)=23[2a+(22)][/tex]
⇒ [tex]4646=46a+506[/tex]
⇒ [tex]4646-506=2a[/tex]
⇒ [tex]4140=2a\\[/tex]
⇒ [tex]a=\frac{4140}{46}[/tex]
⇒ [tex]a=90[/tex]
Number of terms is 23. The first term is 90 and the common difference is 1, so the largest of these 23 integers is the last term.
The 23rd term is
⇒ [tex]90+22[/tex]
⇒ [tex]112[/tex]
Hence we can conclude that the largest of these 23 integers of an arithmetic progression is 112.
Learn more about arithmetic progression here
https://brainly.com/question/20385181
#SPJ2
