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In a certain sculpture, coils of wire are arranged in rows.

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In a certain sculpture, coils of wire are arranged in rows. [#permalink]

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In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

A. 22
B. 21
C. 20
D. 19
E. 18
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Re: Sequencing PS Help Needed [#permalink]

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x13069 wrote:
Can anyone help with this one?

In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

1)22
2)21
3)20
4)19
5)18


We have arithmetic progression with common difference \(d=2\), number of terms \(n=10\) and the sum \(S=120\).

The sum of AP \(S=120=n\frac{2a+d(n-1)}{2}=10\frac{2a+2(10-1)}{2}\), where \(a\) is the first term. --> \(120=10\frac{2a+2(10-1)}{2}=10a+90\) --> \(a=3\).

\(a_n=a_{10}=a_1+d(n-1)=3+2(10-1)=21\)

Answer: B.
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Re: In a certain sculpture, coils of wire are arranged in rows. [#permalink]

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New post 19 Jan 2018, 07:40
x13069 wrote:
In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

A. 22
B. 21
C. 20
D. 19
E. 18


Method 1:

Let \(n\) be the number of rings in the final row. Each preceding row is 2 less than the current row going down to 10 rows in total. So,

\(n + n - 2 + n - 6 + n - 8 + n - 10 + n - 12 + n - 14 + n - 16 + n - 18 = 120\)
\(10n - 90 = 120\)
\(10n = 210\)
\(n = 21\)

Method 2:

We know that

Average * number of terms = Sum

putting in values

\(Average = \frac{120}{10} = 12\)

Since there are 10 terms and 2 apart, 5th and 6th term would be 11 and 13 respectively. adding \(4*2 = 8\) to \(13\) would give us the 10th term.
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Re: In a certain sculpture, coils of wire are arranged in rows.   [#permalink] 19 Jan 2018, 07:40
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