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Intern
Joined: 19 May 2016
Posts: 2

Find the 51st term of the series.
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09 Jul 2016, 12:17
A particular series is given by :
A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on...
Find the first term of the A51.
Source: GMAT Paper



Manager
Joined: 27 Jan 2013
Posts: 97
Location: India
GPA: 3.7

Find the 51st term of the series.
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09 Jul 2016, 23:54
A particular series is given by : A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on... Find the first term of the A51. I'll give it a try. Here each term has basically a set of integers. Careful observation reveals 2 things: 1: Each term has last element of it its set as the square of the term number. That is for A2, say n =2 then last element of A2 is n^2=4. Similarly for A3, last element of set is 3^3=9. 2: The number of elements in the set of nth term = n+(n1). For example for A2, n=2 and number of elements in A2 = 2+1=3. Similarly for A3, n=3 hence number of elements in set of A3 = 3+2 =5. These 2 observations reveal that A51 will have 51+50 = 101 terms and the last term of A51 will be 51^2 and moving backwards each previous terms would be 1 less. Hence A51 = {........,.,.,.,,.,.....,(51^22), (51^21), (51^2) } And the first term of A51 will be 51^2100. Please give kudos if this helps !



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Concentration: General Management, Strategy
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Find the 51st term of the series.
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24 Jul 2016, 09:05
moghi wrote: A particular series is given by :
A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on...
Find the first term of the A51.
Source: GMAT Paper Since we need to find out the first term, we can write all the first terms as T(N)=1+2+5+10+17+.......T(51)>(1) ..................................................... ............................... Again T(N)= 1+2+5+10+..........T(50) +T(51)>(2) Subtract 2 from 1 We get 0=1+1+3+5+7+........()T(51), taking T(51) at the other side we have T(51)= 1+ (1+3+5+7+.....), calculate the sum to n terms of the A.P 1+ 50/2 (2+49*2)=2501 (ANSWER)..Please let me know if you have any questions. Thanks!



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Joined: 16 Oct 2010
Posts: 8788
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Re: Find the 51st term of the series.
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27 Jul 2016, 21:00
moghi wrote: A particular series is given by :
A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on...
Find the first term of the A51.
Source: GMAT Paper Note that A1 has the first positive integer. A2 has next 3, A3 has next 5, A4 has next 7 and so on... To get the first term of A5, we discard the first 1 + 3 + 5 + 7 integers. Similarly, to get the first term of A51, we will need to discard the first 1 + 3 + 5 + 7 + 9 + ... + (50 terms) integers This is an AP and its sum is n/2(2a + (n1)d) = (50/2) * (2*1 + 49*2) = 2500 So when we discard 2500 integers, the fist term of A51 will be 2501.
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Intern
Joined: 29 Apr 2011
Posts: 37

Re: Find the 51st term of the series.
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29 Jul 2016, 07:13
moghi wrote: A particular series is given by :
A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on...
Find the first term of the A51.
Source: GMAT Paper My attempt to make the solution simple. Note each term of the beginning of the series follows the rule An = (n1)^2+1 n>1 A2 = (21)^2+1 = 2.....A4=(41)^2+1=10.....you can check for A3 too A51= (511)^2 +1 = 50^2+1 = 2501 SouthCity



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Joined: 10 May 2018
Posts: 34

Re: Find the 51st term of the series.
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30 Oct 2018, 12:36
moghi wrote: A particular series is given by :
A1 = {1} A2 = {2,3,4} A3 = {5,6,7,8,9} A4 = {10,11,12,13,14,15,16} and so on...
Find the first term of the A51.
Source: GMAT Paper A51 will have the last term as 50^2 = 2500 A51 will have the last term as 51^2 = 2601 Hence, A51 is 2501, 2502....2601




Re: Find the 51st term of the series. &nbs
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30 Oct 2018, 12:36






