S_n represents the sum of the first n terms of sequence X. I

Question

S_n  represents the sum of the first  n  terms of sequence X. If  S_n = n^2 – 6n + 9 , what is the value of 13th term of sequence X?

(A) -80
(B) 100/13
(C) 19
(D) 81
(E) 100

BrentGMATPrepNow · Accepted Answer

Notice that   S_13 = term_1 + term_2 + term_3 + . . . term_{12} + term_{13}  
And   S_{12} = term_1 + term_2 + term_3 + . . . term_{11} + term_{12}  
So,   S_{13}    -    S_{12}    = term_{13}

S_{13} = 13^2 – 6(13) + 9 = 100  
  S_{12}= 12^2 – 6(12) + 9 = 81  
 Aside: By recognizing x² – 6x + 9 = (x-3)², I could have saved myself a  little bit  of time calculating each sum  
So,  term_{13} = 100 - 81 - 19

Answer: D

av1901 · Answer

S_n = x^2 – 6x + 9  = (x-3)^2
We need to find the 13th term of the sequence = S(First 13 terms) - S(First 12 terms) = (13-3)^2 - (12-3)^2 = 10^2 - 9^2 = 19

Answer - C

ScottTargetTestPrep · Answer

I think the question meant to say S_n = n^2 - 6n + 9.

Notice that n^2 - 6n + 9 = (n - 3)^2. So, S_n = (n - 3)^2.

Notice also that the 13th term of the sequence is the difference between the sum of the first 13 terms of the sequence (which is S_13) and the sum of the first 12 terms of the sequence (which is S_12). So the question is to calculate the value of S_13 - S_12.

\Rightarrow  S_13 - S_12

\Rightarrow  (13 - 3)^2 - (12 - 3)^2

\Rightarrow  10^2 - 9^2

\Rightarrow  (10 - 9)(10 + 9) = 1 * 19 = 19

Answer: C

BrentGMATPrepNow · Answer

Thanks for the heads up, Scott! I've edited the question.

Cheers,
Brent

hereiam2410 · Answer

S1= 4
S2= 1 
Hence a1=4, a2=1-4=-3

d=a2-a1=-3-4= -7

an= a+(n-1)d
a13=4+12*-7
 =4-84
 = -80

Why is this incorrect?

Krunaal · Answer

It is  nowhere mentioned  that sequence X is in an AP.

bumpbot · Answer

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S_n represents the sum of the first n terms of sequence X. I

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