In an increasing sequence, the difference between any two successive

Question

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

A. 39
B. 57
C. 66
D. 93
E. 145

DisciplinedPrep · Answer

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

gracie · Answer

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

2asc · Answer

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

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

ravitejab1 · Answer

I have the same doubt. Can some one please clarify?

ManifestDreamMBA · Answer

First term is a, d = 2a
terms will be a,3a,5a,...
sum will be ka (where k is some integer 1+3+5+...)
If we consider 10.2, the sum 135 should have been a multiple of 10.2 but 135/10.2 = 13.xx (which isn't an integer). hence 10.2 isn't possible

If we consider a =15, we don't get 51 as 3rd value or even any nth value (15+30+30 = 75). Same case with 21

Hope this helps!

In an increasing sequence, the difference between any two successive

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