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# If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =  [#permalink]

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02 Apr 2018, 00:56
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Difficulty:

35% (medium)

Question Stats:

73% (02:39) correct 27% (03:08) wrong based on 63 sessions

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If S is the infinite sequence such that $$t_1 = 4$$, $$t_2 = 10$$, …, $$t_n = t_{n-1} + 6$$,…, what is the sum of all the terms from $$t_{10}$$ to $$t_{18}$$?

(A) 671
(B) 711
(C) 738
(D) 826
(E) 991

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Joined: 07 Dec 2017
Posts: 868
If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =  [#permalink]

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02 Apr 2018, 01:10
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1
Bunuel wrote:
If S is the infinite sequence such that $$t_1 = 4$$, $$t_2 = 10$$, …, $$t_n = t_{n-1} + 6$$,…, what is the sum of all the terms from $$t_{10}$$ to $$t_{18}$$?

(A) 671
(B) 711
(C) 738
(D) 826
(E) 991

As there are specific rules for straightforward calculation of sums of arithmetic sequences, we'll use them.
This is a Precise approach.

To calculate the sum of an arithmetic sequence, we need to know the first number, the last number and the number of elements in the sequence.
Our first number is t_10 which is equal to t_1 + d*9 = 4 + 6*9 = 58.
Our last number is t_18 which is equal to t_10 + d*8 = 58 + 6*8 = 106
As there are 9 total elements, our sum is (58+106)*9/2 = 164*9/2 = 82*9 = 82(10 - 1) = 820-82 = 738

Note that as all elements of our sequence are even, we could also have eliminated (A), (B), (E) without calculation and then guessed bewteen (C) and (D).
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Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =  [#permalink]

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02 Apr 2018, 01:55
Bunuel wrote:
If S is the infinite sequence such that $$t_1 = 4$$, $$t_2 = 10$$, …, $$t_n = t_{n-1} + 6$$,…, what is the sum of all the terms from $$t_{10}$$ to $$t_{18}$$?

(A) 671
(B) 711
(C) 738
(D) 826
(E) 991

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8805
Location: Pune, India
Re: If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =  [#permalink]

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02 Apr 2018, 04:56
Bunuel wrote:
If S is the infinite sequence such that $$t_1 = 4$$, $$t_2 = 10$$, …, $$t_n = t_{n-1} + 6$$,…, what is the sum of all the terms from $$t_{10}$$ to $$t_{18}$$?

(A) 671
(B) 711
(C) 738
(D) 826
(E) 991

$$t_{10}$$ to $$t_{18}$$ can be considered an AP with first term as $$t_{10}$$, common difference as 6 and with total 9 terms.

The first term, $$t_{10} = t_1 + 9*6 = 58$$

Sum of 9 terms of AP with first term as 60 is

$$(n/2) * [2a + (n - 1)*d] = (9/2)*[116 + 8*6] = 9*82 = 738$$

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Karishma
Veritas Prep GMAT Instructor

Re: If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) = &nbs [#permalink] 02 Apr 2018, 04:56
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