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03 Oct 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (01:58) correct
31%
(01:47)
wrong
based on 198
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of p; if the sum of consecutive odd numbers from 1 to p, inclusive equals 225?
(A) 15
(B) 21
(C) 29
(D) 31
(E) 33
(A) 15
(B) 21
(C) 29
(D) 31
(E) 33
03 Oct 2024, 02:37
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This is an Arithmetic progression of \(n\) terms with first term, \(a=1\) difference, \(d=2\).
Sum of AP, \(S=\frac{n}{2}[2a+(n-1)*d]=\frac{n}{2}[2+2n-2]=n^2\)
Sum of \(p\) consecutive odd numbers starting from 1 is \(p^2\)
\(p^2=225;p=15\)
\(p^{th}\text{ term}=a+(p-1)*d=1+14*2=29\)
Answer: C
Sum of AP, \(S=\frac{n}{2}[2a+(n-1)*d]=\frac{n}{2}[2+2n-2]=n^2\)
Sum of \(p\) consecutive odd numbers starting from 1 is \(p^2\)
\(p^2=225;p=15\)
\(p^{th}\text{ term}=a+(p-1)*d=1+14*2=29\)
Answer: C
General Discussion
03 Oct 2024, 10:05
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We have a set of consecutive inetegers from 1 to p
ie a sequence (let's call it S) with elements incermenting by 2
average (S) = sum (S) / number of elements of (S)
average of a sequence = (max+min)/2
1- p =15 so average (1+15)/2=8 which is not equal to 225/8
2- same as 1
3- average = (29+1)/2 = 15 and 225/15=15
answer C.
ie a sequence (let's call it S) with elements incermenting by 2
average (S) = sum (S) / number of elements of (S)
average of a sequence = (max+min)/2
1- p =15 so average (1+15)/2=8 which is not equal to 225/8
2- same as 1
3- average = (29+1)/2 = 15 and 225/15=15
answer C.
