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Each term of a certain sequence is calculated by adding a particular

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New post 30 Jul 2018, 00:45
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Each term of a certain sequence is calculated by adding a particular constant to the previous term. The 2nd term of this sequence is 27 and the 5th term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8

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Each term of a certain sequence is calculated by adding a particular  [#permalink]

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New post 30 Jul 2018, 10:41
Bunuel wrote:
Each term of a certain sequence is calculated by adding a particular constant to the previous term. The 2nd term of this sequence is 27 and the 5th term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8


let the constant be \(d\) and the first term be \(a\)

so 2nd term \(= a+d=27\) and 5th term will be \(a+4d=84\). Subtract the two equations to get

\(3d=57 =>d=19\)

Hence \(a=27-19=8\)

Option \(E\)
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Each term of a certain sequence is calculated by adding a particular  [#permalink]

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New post Updated on: 31 Jul 2018, 17:11
Bunuel wrote:
Each term of a certain sequence is calculated by adding a particular constant to the previous term. The 2nd term of this sequence is 27 and the 5th term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8


let d=difference between terms
84-27=57=3d
d=19
27-19=8=1st term
E

Originally posted by gracie on 30 Jul 2018, 18:15.
Last edited by gracie on 31 Jul 2018, 17:11, edited 1 time in total.
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Re: Each term of a certain sequence is calculated by adding a particular  [#permalink]

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New post 30 Jul 2018, 19:34
Bunuel wrote:
Each term of a certain sequence is calculated by adding a particular constant to the previous term. The 2nd term of this sequence is 27 and the 5th term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8


Let the first term be 'a' and the constant being added be d.

So, 2nd term becomes -
\(a_2\) = a + d = 27 ------ (1)

and the 5th term becomes -
\(a_5\) = a + d + d + d + d = 84
Hence,
\(a_5\) = a + 4d = 84 ------ (2)

Now multiplying equation (1) by 4 to eliminate d

hence (1) becomes -

\(a_2\) * 4 =>
4a + 4d = 108 ---- (3)

Subtracting equation (2) from (3)

4a + 4d - a - 4d = 108 - 84

3a = 24

a = 8

Hence answer is E

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Re: Each term of a certain sequence is calculated by adding a particular  [#permalink]

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New post 01 Aug 2018, 16:36
Bunuel wrote:
Each term of a certain sequence is calculated by adding a particular constant to the previous term. The 2nd term of this sequence is 27 and the 5th term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8



Let n = the constant added to each term to get the next term.

We have:

2nd term = 27

3rd term = 27 + n

4th term = 27 + 2n

5th term = 27 + 3n

Since we are given that the 5th term is 84, we have:

27 + 3n = 84

3n = 57

n = 19

Since the second term was given as 27, we know the first term is 27 - n. So the first term is 27 - 19 = 8.

Answer: E
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Re: Each term of a certain sequence is calculated by adding a particular &nbs [#permalink] 01 Aug 2018, 16:36
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