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term after the first term is equal to the preceding term
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18 Jan 2016, 02:25
18 Jan 2016, 02:25
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Question Stats:
76% (02:15) correct
23% (01:59) wrong based on 121 sessions
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\(a_1, a_2, a_3 ................ a_n\)
In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If \(a_1+a_3+a_5=27\), what is the value of \(a_2+a_4\) ?
\(a_2+a_4=\)
In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If \(a_1+a_3+a_5=27\), what is the value of \(a_2+a_4\) ?
\(a_2+a_4=\)
Show: :: OA
18
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Re: term after the first term is equal to the preceding term
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05 Feb 2019, 12:13
05 Feb 2019, 12:13
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sandy wrote:
\(a1, a2, a3 ................ an\)
In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If \(a1+a3+a5=27\), what is the value of \(a2+a4\) ?
\(a2+a4=\)
In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If \(a1+a3+a5=27\), what is the value of \(a2+a4\) ?
\(a2+a4=\)
Show: :: OA
18
By definition:
a1 = a1
a2 = a1 + c
a3 = a1 + c + c = a1 + 2c
a4 = a1 + c + c + c = a1 + 3c
a5 = a1 + c + c + c + c = a1 + 4c
GIVEN: a1+a3+a5=27
We can write: a1 + (a1 + 2c) + (a1 + 4c) = 27
Simplify: 3a1 + 6c = 27
Divide both sides by 3 to get: a1 + 2c = 9
What is the value of \(a2+a4\)
a2 + a4 = (a1 + c) + (a1 + 3c)
= 2a1 + 4c
= 2(a1 + 2c)
= 2(9)
= 18
Answer: 18
Cheers,
Brent
General Discussion
Re: term after the first term is equal to the preceding term
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18 Jan 2016, 04:52
18 Jan 2016, 04:52
3
Expert Reply
Solution
This is clearly an arithmetic progression and we just need the first 5 terms. We can rewrite the progression as a - 2c, a - c, a , a + c, a + 2c. Here the difference between the terms is c as described in the problem
a1 + a3 + a5 = a - 2c + a + a+ 2c = 3a = 27. Hence a =9.
To find a2 + a4 = a - c + a + C = 2a =18.
The purpose of writing this series in the above form is to eliminate c as a variable. Hence answer is 18.
This is clearly an arithmetic progression and we just need the first 5 terms. We can rewrite the progression as a - 2c, a - c, a , a + c, a + 2c. Here the difference between the terms is c as described in the problem
a1 + a3 + a5 = a - 2c + a + a+ 2c = 3a = 27. Hence a =9.
To find a2 + a4 = a - c + a + C = 2a =18.
The purpose of writing this series in the above form is to eliminate c as a variable. Hence answer is 18.
