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

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

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New post 02 Apr 2018, 01:56
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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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If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) =  [#permalink]

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New post 02 Apr 2018, 02:10
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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

(C) is our answer.

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

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New post 02 Apr 2018, 02:55
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


Check NEWEST addition to Ultimate GMAT Quantitative Megathread:

'Sequences Made Easy - All in One Topic!'


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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 02 Apr 2018, 05:56
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

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

Answer (C)
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Re: If S is the infinite sequence such that t(1) = 4, t(2) = 10, …, t(n) = &nbs [#permalink] 02 Apr 2018, 05:56
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