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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul

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A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul [#permalink]

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29 Jan 2019, 02:37

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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

Spoiler: OA

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Re: A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul [#permalink]

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29 Jan 2019, 02:57

Bunuel wrote:

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

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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Re: A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul [#permalink]

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06 Feb 2019, 20:47

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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Joined: 17 Jul 2017

Posts: 194

Re: A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul [#permalink]

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06 Feb 2019, 21:07

Bunuel wrote:

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

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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Re: A sequence is such that a1=1, an=a(n-1)+n. Which of the following coul [#permalink]

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06 Feb 2019, 21:25

kchen1994 wrote:

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

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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