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655-705 (Hard)|   Sequences|      
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Bunuel
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 29 Jan 2019, 02:37
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55% (hard)

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67% (02:20) correct 33% (02:17) wrong based on 188 sessions

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A sequence is such that \(a_1=1\) and \(a_n=a_{n-1}+n\). Which of the following could be the sum of two consecutive terms of the sequence?

A. 60
B. 64
C. 72
D. 80
E. 99
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B
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 06 Feb 2019, 21:07
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Bunuel
A sequence is such that \(a_1=1\) and \(a_n=a_{n-1}+n\). Which of the following could be the sum of two consecutive terms of the sequence?

A. 60
B. 64
C. 72
D. 80
E. 99
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Soln:
a1=1
a2=a1+2=3
a3=a2+3=6
a4=10
a5=15
a6=21.......nd so on

Now a1+a2=4=2^2
a2+a3=9=3^2
a3+a4=16=4^2
so on..
so sum of two consecutive terms will be square of some number.
only b option i.e 64 is 8 ^2 so others can be elimanted.
Hence,answer B.
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 29 Jan 2019, 02:57
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Bunuel
A sequence is such that \(a_1=1\) and \(a_n=a_{n-1}+n\). Which of the following could be the sum of two consecutive terms of the sequence?

A. 60
B. 64
C. 72
D. 80
E. 99
Show more

using expression
a1=1
a2=3
a3=6
a4=10
we observe that for each successive term the value is increasing by same value as value of n
so a5= 15
a6=21
a7=28
a8=36

a7+a8 = 28+36 = 64 IMO B
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 06 Feb 2019, 20:47
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I don't understand this question. If we say each term increases by 2 (n=2), we get can get almost any value in the answer choices. For example 31 + 33 = 64 or 39 + 41 = 80
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 06 Feb 2019, 21:25
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kchen1994
I don't understand this question. If we say each term increases by 2 (n=2), we get can get almost any value in the answer choices. For example 31 + 33 = 64 or 39 + 41 = 80
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kchen1994

Actually each term is not increasing by 2, it is increasing by the term n, said that

a_1 = 1

a_2 = a_1 + 2

a_3 = a_2 + 3

a_4 = a_3 + 4

So if you go on in this series you will notice that pattern, if you calculate the individual terms and add a_7 and a_8 you can get the answer as B
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 27 Aug 2023, 19:52
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Bunuel
A sequence is such that \(a_1=1\) and \(a_n=a_{n-1}+n\). Which of the following could be the sum of two consecutive terms of the sequence?

A. 60
B. 64
C. 72
D. 80
E. 99
Show more


Observe patterns in sequences.
\(a_n=a_{n-1}+n\)
\(a_2=a_{1}+2=1+2\)
\(a_3=a_{2}+3=1+2+3\)
Thus each number is sum of positive integers till n

We are looking at \(a_n+a_{n-1}\)
\(1+2+3+….+n+1+2+3+…..+(n-1)\)
\(2(1+2+3+….+(n-1))+n\)
\(2*\frac{n(n-1)}{2}+n=n^2-n+n=n^2\)
So, sum has to be a square.

Only 64 fits in.

B
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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul 01 Oct 2024, 09:48
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