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term after the first term is equal to the preceding term

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sandy
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term after the first term is equal to the preceding term [#permalink] New post   18 Jan 2016, 02:25
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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=

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Re: term after the first term is equal to the preceding term [#permalink] New post   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=

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
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Re: term after the first term is equal to the preceding term [#permalink] New post   18 Jan 2016, 04:52
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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.
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Re: term after the first term is equal to the preceding term [#permalink] New post   30 Mar 2016, 09:05
i don't understand where you derive a - 2c and a + 2c from
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Re: term after the first term is equal to the preceding term [#permalink] New post   01 Apr 2016, 02:30
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Lets take a real arithmetic progression:

1, 5, 9 , 13, 17

As you can see any term of the above arithmetic progression is 4 greater than the previous term. 1+4 = 5... 5+4 = 9.... so on

So if we draw parallels with the question above here c = 4. Then we can write the above series taking the middle term 9 into account:
9-2*4, 9-4, 9 , 9+4, 9+2*4
a-2*c, a-c , a , a+c, a+2*c

Thats how Sandy derives the a+2c and a-2c terms
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Re: term after the first term is equal to the preceding term [#permalink] New post   29 Jun 2017, 20:10
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If that is confusing then, you can say a, a+c, a+2c, a+3c, a+4c

a1+a3+a5 = 27

a + a+2c + a+4c = 27
a = 9-2c

now a2 + a4

a+c + a+3c
2a+4c
2(9-2c) + 4c
18-4c+4c

18/// is the answer.
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Re: term after the first term is equal to the preceding term [#permalink] New post   24 Aug 2024, 19:46
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Re: term after the first term is equal to the preceding term [#permalink]
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