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705-805 (Hard)|   Sequences|      
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henrymba2021
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is Updated on: 10 Feb 2018, 10:35
Originally posted by henrymba2021 on 10 Feb 2018, 09:11.
Last edited by Bunuel on 10 Feb 2018, 10:35, edited 1 time in total.
Renamed the topic and edited the question.
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75% (hard)

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54% (02:04) correct 46% (02:19) wrong based on 464 sessions

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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 10 Feb 2018, 23:44
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henrymba2021
An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13
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Hi..
An arithmetic sequence has same difference between consecutive terms..
So 2p+2-p=4p+3-(2p+2)....
.p+2=2p+1,
So 2p-p=2-1......p=1

Sequence is p, 2p+2, 4p+3.........
Difference in each term = 2p+2-p=p+2=1+2=3..
13 the term = 1+12*3=37
A
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pushpitkc
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 10 Feb 2018, 11:42
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henrymba2021
An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13
Show more

We are given p,2p + 2, and 4p + 3.... as the sequence.
If p = 1, the sequence becomes 1,4,7.....

Here First term(a) = 1, Common difference(d) = 3

Therefore, the 13th member of this sequence must be \(a + 12d = 1 + 12*3 = 1 + 36 = 37\) (Option A)
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 10 Feb 2018, 22:25
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pushpitkc
henrymba2021
An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13

We are given p,2p + 2, and 4p + 3.... as the sequence.
If p = 1, the sequence becomes 1,4,7.....

Here First term(a) = 1, Common difference(d) = 3

Therefore, the 13th member of this sequence must be \(a + 12d = 1 + 12*3 = 1 + 36 = 37\) (Option A)
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hi pushpitkc
why you have chosen P = 1 ...???
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 10 Feb 2018, 22:48
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sobby
pushpitkc
henrymba2021
An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13

We are given p,2p + 2, and 4p + 3.... as the sequence.
If p = 1, the sequence becomes 1,4,7.....

Here First term(a) = 1, Common difference(d) = 3

Therefore, the 13th member of this sequence must be \(a + 12d = 1 + 12*3 = 1 + 36 = 37\) (Option A)

hi pushpitkc
why you have chosen P = 1 ...???
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Hey sobby

When I tried p=2 or 3, the emerging sequence was not having a common difference.
An arithmetic sequence has a common difference. That is the reason I chose p=1
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 07 Sep 2023, 22:29
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Given: An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3.

Asked: What is the 13th member of this sequence?

Common difference = d = (2p + 2) - p = (4p+3) - (2p+2)
p + 2 = 2p + 1
p = 1

Arithmetic sequence = 1, 4, 7...
a = 1
d = 3
n = 13

\(t_13 = a + (n-1)d = 1 + 12*3 = 37\)

IMO A
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 12 Apr 2025, 12:41
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In any sequence, differences between subsequent terms are equal.

(2P+2)-P=(4P-3)-(2P+2). From this equation P=1.

sobby
pushpitkc
henrymba2021
An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13

We are given p,2p + 2, and 4p + 3.... as the sequence.
If p = 1, the sequence becomes 1,4,7.....

Here First term(a) = 1, Common difference(d) = 3

Therefore, the 13th member of this sequence must be \(a + 12d = 1 + 12*3 = 1 + 36 = 37\) (Option A)

hi pushpitkc
why you have chosen P = 1 ...???
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An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is 15 Mar 2026, 21:37
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If someone didn't pay attention (like I Didn't) and scratched their heads about "how to generate the next terms of this series?"
I was not paying attention to the term "Arithmetic Sequence" is same as "Arithmetic Progression" which means the question is simply stating that the terms are in AP.

So, find the common difference and generate T13 as A+12D = 1 + 12(3) = 37. Option A
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