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26 May 2025, 21:44
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\(a_1\): 2
\(d\): 5
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:42) correct
24%
(02:43)
wrong
based on 292
sessions
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Not Attempted Yet
An arithmetic sequence is such that the division of the fifth term by the third term gives a quotient of 1 and leaves a remainder of 10, while the product of the first and third terms equals 24.
In the table, select a value for the first term, \(a_{1}\) of the sequence, and a value for the difference, \(d\), between successive terms of the sequence, that together are consistent with the given information. Make only one selection in each column.
In the table, select a value for the first term, \(a_{1}\) of the sequence, and a value for the difference, \(d\), between successive terms of the sequence, that together are consistent with the given information. Make only one selection in each column.
| \(a_1\) | \(d\) | |
| 2 | ||
| 3 | ||
| 5 | ||
| 7 | ||
| 12 | ||
| 22 |
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Official Answer
\(a_1\): 2
\(d\): 5
poojaarora1818
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27 May 2025, 01:50
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Solution:
1. The division of the fifth term by the third term gives a quotient of 1 and leaves a remainder of 10-- 5th term = 1*3rd term + 10
2. The product of the first and third terms equals 24--1st term*3rd term =24.
Let's take the LCM of 24, that is \(2^{3}\)*3. The only term that fits for the third term is 12, and 1st term is 2. So, from here we can conclude the 5th term in the sequence will be 22. Also, we can notice, the common difference between the 1st and 3rd term or the 3rd and 5th term is 10. So, the successive difference between the terms that fits our answer choice is 5.
The answer for the First dropdown is 2, and the Second dropdown is 5.
1. The division of the fifth term by the third term gives a quotient of 1 and leaves a remainder of 10-- 5th term = 1*3rd term + 10
2. The product of the first and third terms equals 24--1st term*3rd term =24.
Let's take the LCM of 24, that is \(2^{3}\)*3. The only term that fits for the third term is 12, and 1st term is 2. So, from here we can conclude the 5th term in the sequence will be 22. Also, we can notice, the common difference between the 1st and 3rd term or the 3rd and 5th term is 10. So, the successive difference between the terms that fits our answer choice is 5.
The answer for the First dropdown is 2, and the Second dropdown is 5.
Bismuth83
27 May 2025, 12:12
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\(a_{5}\) = \(a_{1}\) +4d
\(a_{3}\) = \(a_{1}\) + 2d
\(a_{5}\) = \(a_{3}\) + 2d
Given:
\(a_{5}\) = 1*\(a_{3}\) + 10
2d = 10
d=5
\(a_{1}\) * ( \(a_{1}\) + 2d) = 24
\(a_{1}\) * (\(a_{1}\) + 10) = 24
\(a_{1}\) = 2
\(a_{3}\) = \(a_{1}\) + 2d
\(a_{5}\) = \(a_{3}\) + 2d
Given:
\(a_{5}\) = 1*\(a_{3}\) + 10
2d = 10
d=5
\(a_{1}\) * ( \(a_{1}\) + 2d) = 24
\(a_{1}\) * (\(a_{1}\) + 10) = 24
\(a_{1}\) = 2
Bismuth83
