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In an increasing sequence, the difference between any two successive

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Joined: 04 Feb 2018
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In an increasing sequence, the difference between any two successive  [#permalink]

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New post 31 Dec 2018, 00:32
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Difficulty:

  95% (hard)

Question Stats:

35% (03:25) correct 65% (02:57) wrong based on 44 sessions

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In an increasing sequence, the difference between any two successive numbers is twice that of the first term of the sequence. If S is a set of 3 successive numbers in this sequence and the largest number in the set S is 51 and the sum of all the numbers in S is 135. What is the 10th number in this sequence?

Options:

A. 39

B. 57

C. 66

D. 93

E. 145

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Re: In an increasing sequence, the difference between any two successive  [#permalink]

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New post 31 Dec 2018, 01:20
1
Let the first term in the sequence be a
Given that the difference between any two successive numbers is twice that of the first term of the sequence. Hence, the common difference (d) = 2a

Let me the three consecutive integers in set S be the (n - 1)th, nth, and (n + 1)th terms
(n - 1)th term = a + (n - 2)2a
nth term = a + (n-1)2a
(n + 1)th term = a + (n)2a
Given that the largest term in S, i,e. the (n + 1)th term is 51. a + (n)2a = 51......equation 1
Again, the sum of all the numbers in S is 135, {a + (n - 2)2a} + {a + (n-1)2a} + {a + (n)2a} = 135.......equation 2
Solving equation 1 & equation 2, we get a = 3 & n = 8
The 10th number in this sequence = a + 9d = a + 18a = 19a (Since d=2a)
Plug in value of a, 19a = 57 (Since a = 3)

Hence the Correct Answer is Option B. 57
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In an increasing sequence, the difference between any two successive  [#permalink]

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New post 31 Dec 2018, 11:04
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disenapati wrote:
In an increasing sequence, the difference between any two successive numbers is twice that of the first term of the sequence. If S is a set of 3 successive numbers in this sequence and the largest number in the set S is 51 and the sum of all the numbers in S is 135. What is the 10th number in this sequence?

Options:

A. 39

B. 57

C. 66

D. 93

E. 145


let x=first term
three terms of S will be 51-4x, 51-2x, 51
3*51-6x=135
x=3
10th term=3+9*6=57
B
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Re: In an increasing sequence, the difference between any two successive  [#permalink]

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New post 31 Dec 2018, 13:30
Correct me if I'm wrong - I think this question is flawed as the first term could have various values.

Option 1 (apparently the correct answer)
Let first term be a
(51-4a)+(51-2a)+51=135; a=3

Option 2
Let first term be a
a+3a+5a=135; a=15

Option 3
let first term be a
51=a+4a; a=10.2

Option 4
Let first term be a
a+3a+51=135; a=21
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In an increasing sequence, the difference between any two successive  [#permalink]

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New post 02 Jan 2019, 03:45
1

Solution


Given:
    • In an increasing sequence, d = 2a
    • S is a set of 3 successive numbers in this sequence
    • Largest number in S = 51, and sum of the three numbers in S = 135

To find:
    • The \(10^{th}\) term of this sequence

Approach and Working:
    • Sum of the three numbers in S = 51 + 51 - d + 51 – 2d = 135
      o Implies, 153 – 3d = 135
      o Thus, d = 6

    • \(t_{10} = a + 9d = \frac{d}{2} + 9d = 57\)

Hence, the correct answer is Option B

Answer: B

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In an increasing sequence, the difference between any two successive   [#permalink] 02 Jan 2019, 03:45
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