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# In the sequence a1, a2, ... , an each term after the first term is

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In the sequence a1, a2, ... , an each term after the first term is  [#permalink]

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Updated on: 11 Nov 2017, 17:44
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Difficulty:

45% (medium)

Question Stats:

81% (02:14) correct 19% (02:24) wrong based on 48 sessions

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In the sequence $$a_1$$, $$a_2$$, ... ,$$a_n$$ each term after the first term is equal to the preceding term plus a constant c.

$$a_1$$ + $$a_{11}$$ + $$a_{21}$$ = 99. What is the value of $$a_3$$+$$a_{19}$$?

A. 66
B. 44
C. 33
D. 22
E. 11

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Originally posted by Gnpth on 10 Nov 2017, 18:26.
Last edited by Gnpth on 11 Nov 2017, 17:44, edited 2 times in total.
formatted the choices
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Posts: 7334
Re: In the sequence a1, a2, ... , an each term after the first term is  [#permalink]

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10 Nov 2017, 19:09
Gnpth wrote:
In the sequence $$a_1$$, $$a_2$$, ... ,$$a_n$$ each term after the first term is equal to the preceding term plus a constant c.

$$a_1$$ + $$a_{11}$$ + $$a_{21}$$ = 99. What is the value of $$a_3$$+$$a_{19}$$?

A. 33
B. 66
C. 22
D. 44
E. 11

Hi..

As each term is C more than the previous one...
Each term, $$a_x$$ will be (x-1) times c more than $$a_1$$
So $$a_1+a_{11}+a_{21}=a_1+a_1+(11-1)+a_1+(21-1)=3*a_1+30=99....a_1=23$$

Now $$a_3+a_{19}=a_1+(3-1)+a_1+(19-1)=2*a_1+20=2*23+20=66$$

B

But the choices require formatting as per the GMAT. All choices are to be some order then 66 becomes choice A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: In the sequence a1, a2, ... , an each term after the first term is  [#permalink]

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10 Nov 2017, 19:26
1
Gnpth wrote:
In the sequence $$a_1$$, $$a_2$$, ... ,$$a_n$$ each term after the first term is equal to the preceding term plus a constant c.

$$a_1$$ + $$a_{11}$$ + $$a_{21}$$ = 99. What is the value of $$a_3$$+$$a_{19}$$?

A. 66
B. 44
C. 33
D. 22
E. 11

a2 = a1 + c, a3 = a2+c = a1+2c
a11 = a1+10C, a21 = a1+20c
3a1 + 30c = 99, a1+10c =33

a3+a19 = 2a1+20c = 2(a1+10c)=66
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Re: In the sequence a1, a2, ... , an each term after the first term is  [#permalink]

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18 Feb 2019, 17:39
Pn = Pn-1 + C (constant)

It is an arithmetic progression:

Sum = (Average)(n)

A1 + A11 + A21 = 99

99/3 = 33 (Average)

Sum = (33)(2) ... 2 terms (A3 + A19)

Sum = 66

A
Re: In the sequence a1, a2, ... , an each term after the first term is   [#permalink] 18 Feb 2019, 17:39
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