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# Given an arithmetic sequence of N terms in which the common difference

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
Given an arithmetic sequence of N terms in which the common difference [#permalink]

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26 Mar 2018, 23:26
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Given an arithmetic sequence of N terms in which the common difference between terms is 2, what is the value of N?

(1) The first term is 18.
(2) The last term is 70.
[Reveal] Spoiler: OA

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Joined: 16 Sep 2016
Posts: 207
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Re: Given an arithmetic sequence of N terms in which the common difference [#permalink]

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27 Mar 2018, 00:17
Bunuel wrote:
Given an arithmetic sequence of N terms in which the common difference between terms is 2, what is the value of N?

(1) The first term is 18.
(2) The last term is 70.

Some theory on the AP (arithmetic progressions)

$$x_n = a+d (n-1)$$

Where x_n is the nth term. a is the first term, n is the number of terms & d is the common difference.

So here we are asked to find the no. of terms or n.

(1) The first term is 18. We do not know how long the series is just based on the starting point. Not sufficient
(2) The last term is 70. We do not know how long the series is just based on the ending point. Not sufficient

At this point it can be either (C) both options together work or (E) nothing works.

Let's see,
(1) + (2) -> we know the starting point and the ending point both! Also we are given the difference between any two successive elements. Hence Sufficient.

Option (C) is correct.

Best,
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Joined: 29 Dec 2017
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Given an arithmetic sequence of N terms in which the common difference [#permalink]

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29 Mar 2018, 14:44
Bunuel wrote:
Given an arithmetic sequence of N terms in which the common difference between terms is 2, what is the value of N?

(1) The first term is 18.
(2) The last term is 70.

For any arithmetic sequence a(n)=a1+(n-1)d, and we are given d=2.
So we have 4 variables and 2 equations, and we need 2 more variables/equations to solve the problem.
--> Highly likely that the answer is C

(1) NS, gives us only 1 variable
(2) NS, gives us only 1 variable

(1)+(2) Sufficient, as we got 2 variable, and this is enough.
Given an arithmetic sequence of N terms in which the common difference   [#permalink] 29 Mar 2018, 14:44
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