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03 Apr 2020, 04:53
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A
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:
70% (02:29) correct
30%
(02:37)
wrong
based on 312
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Let \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers with the largest term equal to \(2*a_3\). If the sum of the numbers in the new sequence is 450, then what is the value of \(a_5\) ?
A. 51
B. 49
C. 47
D. 45
E. 43
Are You Up For the Challenge: 700 Level Questions
A. 51
B. 49
C. 47
D. 45
E. 43
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 05:49
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Bunuel
Let the consecutive 5 odd number, {\(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\)} = {\(2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5\)}
Largest term of the even number = \(2*a_3 = 2(2n + 1) = 4n + 2\)
--> Five consecutive even terms = {\(4n - 6\), \(4n - 4\), \(4n - 2\), \(4n\), \(4n + 2\)}
Sum = \(450\)
--> \(4n - 6 + 4n - 4 + 4n - 2 + 4n + 4n + 2 = 450\)
--> \(20n - 10 = 450\)
--> \(20n = 460\)
--> \(n = 23\)
\(a_5 = 2n + 5 = 2*23 + 5 = 51\)
Option A
General Discussion
21 Nov 2022, 14:47
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Sum of odd no.of terms in A.P = no.of terms x middle term.
For even series middle term is (2a3 -4), hence follows---
(2a3 - 4)x5 = 450
a3= 47
Now a5 = a3 + 4 = 47+4= 51.
Hence A is the correct choice.
Posted from my mobile device
For even series middle term is (2a3 -4), hence follows---
(2a3 - 4)x5 = 450
a3= 47
Now a5 = a3 + 4 = 47+4= 51.
Hence A is the correct choice.
Posted from my mobile device
