Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49948

If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
30 Jul 2015, 11:11
Question Stats:
81% (02:00) correct 19% (02:13) wrong based on 177 sessions
HideShow timer Statistics




CEO
Joined: 08 Jul 2010
Posts: 2537
Location: India
GMAT: INSIGHT
WE: Education (Education)

If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
30 Jul 2015, 11:18
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 E. 840
Kudos for a correct solution. nth Term of an Arithmetic Progression, \(T_n = a + (n1)d\)
Sum of n terms, \(S_n = (n/2)*[2a + (n1)*d\)
Where, a = first term of Progression, d = common difference (Second term  first term or Third  second term etc.)4th Term, \(T_4 = a + (41)*d = a+3d\) 12th Term, \(T_{12} = a + (121)*d = a+11d\) Given : (a+11d) + (a+3d) = 8i.e. 2a + 14d = 8 Question : Sum of 15 terms, \(S_{15} = (15/2)*[2a + (151)*d = (15/2)*[2a+14d] = (15/2)*8 = 60\) Answer: Option A
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




Manager
Joined: 14 Mar 2014
Posts: 147

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
30 Jul 2015, 15:03
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 E. 840
Kudos for a correct solution. IMO: A nth term of an AP = a+(n1)dLet 1st term of AP = a+d 12th term of AP = a+11d Sum of 1st & 12th = 8 a+d+a+11d =8 2a+14d=8 a+7d = 4 (i)Sum of 1st 15 terms = (a+d)+(a+2d)+(a+3d)+.....(a+14d) =15a+(d+2d+3d+4d+..14d) = 15a+d(1+2+3+..14) Sum of 1st n natural numbers = \(\frac{n(n+1)}{2}\) = 15a +d (\(\frac{14*15}{2}\)) = 15a +d(7*15) =15(a+7d) (sub eq(i)) =15*4=60
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos ¯\_(ツ)_/¯



Manager
Joined: 25 Nov 2014
Posts: 158
WE: Engineering (Manufacturing)

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
31 Jul 2015, 02:08
Ans = A
4th term + 12th term = 8 i.e., (a+3d)+(a+11d) = 8 2a+14d = 8  (1)
Now, Sum of first 15 terms = (15/2) * [2a + (151)d] = (15/2) * [2a + 14d] = (15/2) * 8  From (1) = 60



Director
Joined: 21 May 2013
Posts: 651

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
31 Jul 2015, 02:35
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 E. 840
Kudos for a correct solution. First term=a, common difference=d 4th term=a+3d 12th term=a+11d Sum=2a+14d=8 Now , sum upto first 15 terms= 15/2(2a+14d)=15/2(8)=60 Answer A



Senior Manager
Joined: 28 Jun 2015
Posts: 293
Concentration: Finance
GPA: 3.5

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
31 Jul 2015, 07:18
Let a = first term, d = common difference. 4th term = a+3d 12th term = a+11d a+3d + a+11d = 8 2a + 14d = 8 a + 7d = 4. Sum of the first 15 terms = 15/2 (2a + 14d) = 15 (a+7d) = 15 (4) = 60. Ans (A).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



Senior Manager
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
05 Aug 2015, 23:49
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 E. 840 Ans: A solution: given that, lets say first term is a and common difference is d then, a+3d+a+11d=8 = a+7d =4 ===this is the 8th term, which will be the median of the set of 15 terms in AP so the sum of all the terms in AP= number of terms*median = 15*4 = 60
_________________
 The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks



Current Student
Joined: 12 Aug 2015
Posts: 2638

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
06 Aug 2016, 00:47



VP
Joined: 07 Dec 2014
Posts: 1103

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
06 Aug 2016, 14:54
t4+t12=8 in AP 1,2,3,4,5.., where a and d=1, t4+t12=2*8 if we assume a and d=1/2, then ∑15=15/2*(1+14*1/2)=60



VP
Joined: 07 Dec 2014
Posts: 1103

If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
24 Aug 2017, 12:20
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 the 8th term is the middle term between the 4th and 12th terms the middle term is half the sum of equidistant terms on either side the 8th term=4 because the 8th term is the middle term of a 15 term progression, it is also the median 4*15=60 A



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3846
Location: United States (CA)

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
29 Aug 2017, 16:15
Bunuel wrote: If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?
A. 60 B. 120 C. 160 D. 240 E. 840 An arithmetic progression (sequence) is characterized by having each term separated from the next term by a common difference. We can let d = the common difference (i.e., the difference between each pair of consecutive terms) and let the first term = a. Thus, the first term is a, second term is a + d, and third term is a +2d, so the 4th term is a + 3d and the 12th term is a + 11d. Thus: (a + 3d) + (a + 11d) = 8 2a + 14d = 8 a + 7d = 4 We are asked to find the sum of the first 15 terms. Since this is an arithmetic progression, we can use the formula sum = quantity x average. The ‘quantity’ is 15 since there are 15 terms. The ‘average’ of a finite arithmetic progression is also the median, which in this case is the 8th term. The 8th term in terms of a and d is a + 7d, and we have found that to be 4. Thus: Sum = 15 x 4 = 60 Answer: A
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
07 Sep 2017, 10:18
We can use the concept of corresponding pairs if the series is in AP. here is what i mean suppose there are 15 terms in AP the sequence is given below is in AP 2 , 4, 6, 8, 10,12,14,16,18,20,22,24,26,28,30 Then the corresponding pairs are (2,30),(4,28), (6,26), (8,24), (10,22), (12,20),(14,18) (16,16).Then the average of any corresponding pairs will be equal to average of the seq. Given that the series is in AP hence in given problem 4 pair corresponds to 12 pair in a sequence of 15 terms The sum of 4 pair and 12 pair is 8 So, sum= 15(8/2)= 60
_________________
Abhimanyu



NonHuman User
Joined: 09 Sep 2013
Posts: 8426

Re: If the sum of the 4th term and the 12th term of an arithmetic progress
[#permalink]
Show Tags
22 Sep 2018, 08:28
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If the sum of the 4th term and the 12th term of an arithmetic progress &nbs
[#permalink]
22 Sep 2018, 08:28






