It is currently 24 Feb 2018, 19:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the sum of the 4th term and the 12th term of an arithmetic progress

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43898
If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

30 Jul 2015, 10:11
Expert's post
14
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:31) correct 23% (01:52) wrong based on 157 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________
SVP
Joined: 08 Jul 2010
Posts: 1959
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, 10:18
Expert's post
2
This post was
BOOKMARKED
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, $$T_n = a + (n-1)d$$

Sum of n terms, $$S_n = (n/2)*[2a + (n-1)*d$$

Where, a = first term of Progression, d = common difference (Second term - first term or Third - second term etc.)

4th Term, $$T_4 = a + (4-1)*d = a+3d$$
12th Term, $$T_{12} = a + (12-1)*d = a+11d$$

Given : (a+11d) + (a+3d) = 8
i.e. 2a + 14d = 8

Question : Sum of 15 terms, $$S_{15} = (15/2)*[2a + (15-1)*d = (15/2)*[2a+14d] = (15/2)*8 = 60$$

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Joined: 14 Mar 2014
Posts: 148
GMAT 1: 710 Q50 V34
Re: If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

30 Jul 2015, 14:03
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+(n-1)d
Let 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: 164
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, 01:08
1
KUDOS
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 + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 8 --------------- From (1)
= 60
Director
Joined: 21 May 2013
Posts: 581
Re: If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

31 Jul 2015, 01:35
1
KUDOS
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
Senior Manager
Joined: 28 Jun 2015
Posts: 298
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, 06:18
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.

Manager
Joined: 21 Jan 2015
Posts: 149
Location: India
Concentration: Strategy, Marketing
WE: Marketing (Consumer Products)
Re: If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

05 Aug 2015, 22:49
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.
Thanks

Retired Moderator
Joined: 12 Aug 2015
Posts: 2430
GRE 1: 323 Q169 V154
Re: If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

05 Aug 2016, 23:47
Nice Question
Here A4+A12 =8
hence 2A+14D=8 => A+7D=4
Now S(15)= 15/2 [2A+14D] => 15[A+7D] = 15*4 = 60
Smash A
_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Director
Joined: 07 Dec 2014
Posts: 907
Re: If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

06 Aug 2016, 13:54
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
Director
Joined: 07 Dec 2014
Posts: 907
If the sum of the 4th term and the 12th term of an arithmetic progress [#permalink]

### Show Tags

24 Aug 2017, 11:20
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: 2192
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, 15:15
1
KUDOS
Expert's post
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study 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, 09:18
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

Re: If the sum of the 4th term and the 12th term of an arithmetic progress   [#permalink] 07 Sep 2017, 09:18
Display posts from previous: Sort by