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Is the sum of 7th through 18th term in a sequence of integers even?

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Is the sum of 7th through 18th term in a sequence of integers even? [#permalink]

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New post 09 Apr 2018, 14:41
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Is the sum of \(7^{th}\) through \(18^{th}\) term in a sequence of integers even?

(1) Every term in the sequence is 5 more than the previous term.
(2) The \(1^{st}\) term in the sequence is 5.

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[Reveal] Spoiler: OA
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Re: Is the sum of 7th through 18th term in a sequence of integers even? [#permalink]

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New post 09 Apr 2018, 23:36
Sum= Sum of first 18 terms- Sum of first 6 terms
Sum of first 18 terms=9(2a+17d)
Sum of first 6 terms=3(2a+5d)
Sum=18a+153d-6a-15d= 12a+138d
Sum is even. I don't need any other info.

Please point out my mistake
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Re: Is the sum of 7th through 18th term in a sequence of integers even? [#permalink]

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New post 10 Apr 2018, 22:38
We can also say that in all we want some of 12 terms i.e. from 7th to 18th

i)consider 7th term as odd
Then 6 terms will be odd and other will be even.
So sum would always be even as 6 odd terms always give even and other 6 even also give even so total sum would be even.

ii) if 7th term is odd then also 6 odd and 6 even terms.Same logic follows as above.

So A is answer as we need to know differnce between 2 terms.initial term does not matter

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Re: Is the sum of 7th through 18th term in a sequence of integers even?   [#permalink] 10 Apr 2018, 22:38
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Is the sum of 7th through 18th term in a sequence of integers even?

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