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# nth term of an AP, consisting of only positive integers, is denoted by

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Manager
Joined: 13 Jan 2018
Posts: 67
Location: India
GMAT 1: 580 Q47 V23
GPA: 4
nth term of an AP, consisting of only positive integers, is denoted by  [#permalink]

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26 Oct 2018, 05:10
3
00:00

Difficulty:

55% (hard)

Question Stats:

43% (01:02) correct 57% (02:00) wrong based on 21 sessions

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$$n_{th}$$ term of an AP, consisting of only positive integers, is denoted by $$a_n$$. It is given that $$a_3 = 4$$ and $$a_{n-2} = 9$$. What is the value of $$(a_n + 2n +2)$$

A. 31
B. 32
C. 33
D. 34
E. 35
Manager
Joined: 14 Jun 2018
Posts: 179
Re: nth term of an AP, consisting of only positive integers, is denoted by  [#permalink]

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26 Oct 2018, 11:46
Mean of the AP = (9+4)/2 = 6.5
Sum of first and last term = 13

Case 1
First term : 1 ; Last Term 12 ; Common Diff = 1
This isn't possible because 3rd term will be 3 whereas question says it's 4.

Case 2
First term : 2 ; Last Term 11; CD = 1
This is possible
No of terms = 10 = n
Last term = 11
11 + 20 + 2 = 33
Option C
Intern
Joined: 18 May 2017
Posts: 2
Re: nth term of an AP, consisting of only positive integers, is denoted by  [#permalink]

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27 Oct 2018, 20:23
This is a very poor and unclear question!
Re: nth term of an AP, consisting of only positive integers, is denoted by &nbs [#permalink] 27 Oct 2018, 20:23
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