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# In a sequence of numbers in which the difference of any two successive

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Math Expert
Joined: 02 Sep 2009
Posts: 65290
In a sequence of numbers in which the difference of any two successive  [#permalink]

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15 May 2020, 00:15
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25% (medium)

Question Stats:

82% (02:51) correct 18% (02:56) wrong based on 27 sessions

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In a sequence of numbers in which the difference of any two successive terms is a constant, the second term is 8 and the eighths term is 2 more than thrice the second term. What is the sum of the first eight terms of this sequence?

A. 124
B. 110
C. 108
D. 106
E. 96

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Re: In a sequence of numbers in which the difference of any two successive  [#permalink]

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15 May 2020, 00:43
1
Bunuel wrote:
In a sequence of numbers in which the difference of any two successive terms is a constant, the second term is 8 and the eighths term is 2 more than thrice the second term. What is the sum of the first eight terms of this sequence?

A. 124
B. 110
C. 108
D. 106
E. 96

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If the first term = a
COmmon difference = d

Then, Second Term = a+d = 8
Then, Eigth Term = a+7d = 3*(a+d)+2

i.e. a+7d = 3*(a+d)+2
i.e. 2a+2 = 4d
i.e. a +1 = 2d i.e .a = 2d - 1

Also, a+d = 8

i.e. (2d-1)+d = 8

i.e. d = 3
and a = 5

First 8 terms are {5, 8, 11, 14, 17, 20, 23, 26}

Sum of terms in A.P. = (n/2)[First term+Last Term] = (8/2)*(5+26) = 4*31 = 124

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In a sequence of numbers in which the difference of any two successive  [#permalink]

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15 May 2020, 01:36
1
Bunuel wrote:
In a sequence of numbers in which the difference of any two successive terms is a constant, the second term is 8 and the eighths term is 2 more than thrice the second term. What is the sum of the first eight terms of this sequence?

A. 124
B. 110
C. 108
D. 106
E. 96

Solution

• Since the difference of any two successive terms is a constant, so the given sequence is in Arithmetic progression.
• Now, let us assume that the first term of the A.P. is a and the common difference is d.
• Second term $$= a + d = 8 …………Eq.(i)$$
• Eighth term $$= a + 7d = 3*8 + 2 = 26 ….Eq.(ii)$$
• Subtracting second term from eighth term(or, Eq.(i) from Eq.(ii)) , we get,
o $$6d = 18 ⟹ d = 3$$
o Thus, $$a = 8 – 3 = 5$$
• Therefore, the sum of first eight terms of the sequence $$= \frac{8}{2}[5 + 26] = 4*31 = 124$$
Thus, the correct answer is Option A.
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Re: In a sequence of numbers in which the difference of any two successive  [#permalink]

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16 May 2020, 01:05
1
See the attachment. Answer is A

Attachments

1.PNG [ 18.28 KiB | Viewed 178 times ]

Re: In a sequence of numbers in which the difference of any two successive   [#permalink] 16 May 2020, 01:05