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moghi
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 + (n-1)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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moghi
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 = (n-1)^2+1 n>1

A2 = (2-1)^2+1 = 2.....A4=(4-1)^2+1=10.....you can check for A3 too

A51= (51-1)^2 +1 = 50^2+1 = 2501

-SouthCity
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moghi
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
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Hello from the GMAT Club BumpBot!

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