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Sequence

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Wed Jul 28, 2010 2:22 pm
selango wrote:What is the sixtieth term in the following sequence?

1, 2, 4, 7, 11, 16, 22...

(A) 1,671
(B) 1,760
(C) 1,761
(D) 1,771
(E) 1,821

OA D
term 1: 1
term 2: 2 = 1+1
term 3: 4 = 1+1+2
term 4: 7 = 1+1+2+3
term 5: 11 = 1+1+2+3+4
.
.
.
term 60 = 1+1+2+3+4+. . . . +59
So, we need to find the sum of 1+2+3+4+. . . . +59

Now, there is a nice rule for finding the sum of numbers from 1 to n.
It is 1+2+3+...+n = n(n+1)/2
So, 1+2+3+...+59 = 59(60)/2 = 59(30) = 1770

Put it all together, we get: term 60 = 1+1+2+3+4+. . . . +59
= 1+ 1770
= 1771
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by selango » Thu Jul 29, 2010 12:46 am
Any other approach?
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by kvcpk » Thu Jul 29, 2010 1:36 am
selango wrote:What is the sixtieth term in the following sequence?

1, 2, 4, 7, 11, 16, 22...

(A) 1,671
(B) 1,760
(C) 1,761
(D) 1,771
(E) 1,821

OA D
Look at the difference between the digits in sequence:
it is 1,2,3,4,5,6....
Hence 60th term will be 60 units more than 59th term.
59th term is 59 units more than 58th term.
58th term is 58 units more than 57th term.
...
.
2nd term is 2 units more than 1st term.
1st term = 1
Hence, 60th term = 1+2+3+...60
= 1771
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by GMATGuruNY » Thu Jul 29, 2010 6:48 am
kvcpk wrote:
selango wrote:What is the sixtieth term in the following sequence?

1, 2, 4, 7, 11, 16, 22...

(A) 1,671
(B) 1,760
(C) 1,761
(D) 1,771
(E) 1,821

OA D
Look at the difference between the digits in sequence:
it is 1,2,3,4,5,6....
Hence 60th term will be 60 units more than 59th term.
59th term is 59 units more than 58th term.
58th term is 58 units more than 57th term.
...
.
2nd term is 2 units more than 1st term.
1st term = 1
Hence, 60th term = 1+2+3+...60
= 1771
Fun question, but please note that this is NOT how sequence questions typically are phrased on the GMAT.

On the GMAT, the sequence question above likely would look like this:

A sequence is determined by the equation A(n) = A(n-1) + n - 1 for all n>1. If A(7) = 22, what is the value of A(4)?

A(7) = A(6) + 7 - 1
22 = A(6) + 6
A(6) = 16

A(6) = A(5) + 6 - 1
16 = A(5) + 5
A(5) = 11

A(5) = A(4) + 5 - 1
11 = A(4) + 4
A(4) = 7
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