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# Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co

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Joined: 02 Sep 2009
Posts: 56300
Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co  [#permalink]

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17 Jun 2019, 01:40
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Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 19 members of this sequence?

A. 878
B. 900
C. 788
D. 928
E. 1022

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Re: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co  [#permalink]

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17 Jun 2019, 01:59
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23,27,28,32,33,37..we can see that each pair sums up to be 50, 60, 70 and so on till 130 as there 9 pairs
Hence sums up to be 810 till 18th term
Since we know each pair has a difference of 4 therefore 17th and 18th term = 2x+4 =130
17 th term = 63
Hence 19th term = 63+5 =68
Hence sum = 810+68=878

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Re: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co  [#permalink]

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17 Jun 2019, 02:04
Bunuel wrote:
Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 19 members of this sequence?

A. 878
B. 900
C. 788
D. 928
E. 1022

Let first number = 23
Sequence is 23, 23+4, 23+5, 23+9, 23+10, . . . .
In first 19, there are 10 Odd terms & 9 Even terms
Odd terms $$t_1$$, $$t_3$$, $$t_5$$. . . . . . . .$$t_{19}$$ are 23, 23+5, 23+10 . . . . . . 23+45 --> AP series with common difference 5
Even terms $$t_2$$, $$t_4$$, $$t_6$$. . . . . . . .$$t_{18}$$ are 23+4, 23+9, 23+14, . . . . . . 23+44 --> AP series with common difference 5

Sum of Odd terms = n/2*(1st term + last term) = 10/2*(23 + 68) = 455
Sum of Even terms =9/2*(1st term + last term) = 9/2*(27 + 67) = 9/2*94 = 423
Total sum = 455 + 423 = 878

IMO Option A

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Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co  [#permalink]

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Updated on: 17 Jun 2019, 21:55
This problem consists of two series for
1st Series starting with 23,28.33......10 terms
2nd Series starting with 27,32....9 terms

For 1st series,
total number of terms will be 10
and 1stterm =23 & c.d=5
S1=455

Second series will be of 9 terms,
1st term =27 & c.d=5
S2=423

Sum of series = 423+455=878
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Originally posted by thembaseeker on 17 Jun 2019, 11:46.
Last edited by thembaseeker on 17 Jun 2019, 21:55, edited 1 time in total.
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Posts: 57
Re: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co  [#permalink]

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17 Jun 2019, 18:55
ashudhall wrote:
23,27,28,32,33,37..we can see that each pair sums up to be 50, 60, 70 and so on till 130 as there 9 pairs
Hence sums up to be 810 till 18th term
Since we know each pair has a difference of 4 therefore 17th and 18th term = 2x+4 =130
17 th term = 63
Hence 19th term = 63+5 =68
Hence sum = 810+68=878

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Hey! This is a really easy solution. My only question is that why is it 2x+4=130 and not 2x+5=130 since the stem mentions that the diff between the alternate numbers is 5?
Re: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co   [#permalink] 17 Jun 2019, 18:55
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# Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It co

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