It is currently 17 Oct 2017, 03:11

### 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

# In a certain sequence, the term

Author Message
TAGS:

### Hide Tags

SVP
Joined: 12 Sep 2015
Posts: 1793

Kudos [?]: 2443 [0], given: 356

In a certain sequence, the term [#permalink]

### Show Tags

26 Jan 2017, 12:28
Expert's post
Top Contributor
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:51) correct 21% (02:26) wrong based on 96 sessions

### HideShow timer Statistics

In a certain sequence, the term an is given by the formula an = k + $$\frac{n}{2}$$, where k is a constant. If the sum of all the terms from a1 to a20 inclusive equals 35, what is the value of k?

A) -3.5
B) - 3.2
C) -3
D) -2.8
E) -2.5

*Kudos for all correct solutions
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2443 [0], given: 356

Manager
Joined: 03 Oct 2013
Posts: 84

Kudos [?]: 22 [1], given: 16

Re: In a certain sequence, the term [#permalink]

### Show Tags

26 Jan 2017, 12:37
1
KUDOS
Attachments

Untitled.png [ 81.23 KiB | Viewed 943 times ]

_________________

P.S. Don't forget to give Kudos on the left if you like the solution

Kudos [?]: 22 [1], given: 16

Manager
Joined: 28 May 2014
Posts: 196

Kudos [?]: 133 [0], given: 68

Re: In a certain sequence, the term [#permalink]

### Show Tags

26 Jan 2017, 19:50
1
This post was
BOOKMARKED
Given that An = K + n/2;

Therefore, A1 = K + 1/2; A2 = K + 2/2 ..... A20 = K + 20/2

Sum of A1 to A20 = 20K + 1/2( 1 + 2 + 3 + .... 19 + 20)
=>35 = 20K + 1/2*20 (1+20)/2
=>35 = 20K + 105
=>20K = -70
=>K = -3.5. Ans A

Kudos [?]: 133 [0], given: 68

SVP
Joined: 12 Sep 2015
Posts: 1793

Kudos [?]: 2443 [2], given: 356

Re: In a certain sequence, the term [#permalink]

### Show Tags

27 Jan 2017, 09:09
2
KUDOS
Expert's post
Top Contributor
2
This post was
BOOKMARKED
GMATPrepNow wrote:
In a certain sequence, the term an is given by the formula an = k + $$\frac{n}{2}$$, where k is a constant. If the sum of all the terms from a1 to a20 inclusive equals 35, what is the value of k?

A) -3.5
B) - 3.2
C) -3
D) -2.8
E) -2.5

Let's examine a few terms:
a1 = k + 1/2
a2 = k + 2/2
a3 = k + 3/2
.
.
.
a20 = k + 20/2

So, TOTAL SUM = (k + 1/2) + (k + 2/2) + (k + 3/2) + . . . + (k + 20/2)
= 20k + 1/2 + 2/2 + 3/2 + . . . + 20/2
= 20k + (1/2)(1 + 2 + 3 + . . . + 20)

Sum of first n integers formula: 1 + 2 + 3 + 4 + . . . + n = (n)(n + 1)/2

Applying this formula to the sum 1 + 2 + 3 + . . . + 20, we get:
= 20k + (1/2)[(20)(21)/2 ]
= 20k + 105

We're told that this sum equals 35, so......
35 = 20k + 105
Subtract 105 from both sides: -70 = 20k
Divide both sides by 20 to get: -3.5 = k

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2443 [2], given: 356

Manager
Joined: 22 Nov 2016
Posts: 199

Kudos [?]: 36 [1], given: 38

Location: United States
GPA: 3.4
Re: In a certain sequence, the term [#permalink]

### Show Tags

01 Jul 2017, 12:29
1
KUDOS
Writing down first few numbers of the sequence...

$$a(1)= k+\frac{1}{2}$$
$$a(2)= k+\frac{2}{2}$$
$$a(3)= k+\frac{3}{2}$$
.
.
.

The sum of $$35=20k+\frac{1}{2}*(1+2+....+19+20)$$
$$35 = 20k+\frac{(20*21)}{4}$$
$$35 = 20K+105$$
$$20k=-70$$
$$k=\frac{-7}{2}$$ = -3.5, A
_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 36 [1], given: 38

Intern
Joined: 14 Oct 2016
Posts: 30

Kudos [?]: 6 [0], given: 147

Location: India
WE: Sales (Energy and Utilities)
Re: In a certain sequence, the term [#permalink]

### Show Tags

08 Sep 2017, 20:07
We can find the answer in two methods

First Method:
a(1)= K+1/2, a(2)= K+1 , a(3)=K=3/2 then we see each term is + 1/2 the previous term.

For AP
Sum = n{(2a+(n-1)d}/2
So 35= 20{2a+ (19)*1/2)}/2
Simplifying we get
7=2a+19
So a= -3,
so a(1)= -3= K+1/2
So k= -7/2= -3.5

Second Method:
So each even term will be consecutive integer 1,2,3,4,5,6,7,8,9,10 and each odd term will be fraction with numerators as odd consecutive numbers and denominator as 2
like 1/2, 3/2,5/2,7/2.9/2,11/2,13/2,15/2,17/2,19/2

So the sum will be
35= 20 K + {1+3+5+7+9+11+13+15+17+19}/2 + {1+2+3+4+5+6+7+8+9+10)

Formula for sum of n odd integers where n is odd is {(n+1)/2}^2 and formula for sum of n odd integers where n is even{(n/2)}^2

Say we have to find sum of 19 odd integers . In this case we use formula {(n+1)/2}^2 since n=19 is odd

And formula for sum of n natural numbers is n(n+1)/1

35= 20K +{(19+1)/2}^2+ 10(11)/2

35= 20k +55+50
k= -3.5
_________________

Abhimanyu

Kudos [?]: 6 [0], given: 147

Re: In a certain sequence, the term   [#permalink] 08 Sep 2017, 20:07
Display posts from previous: Sort by