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# The first three terms in an arithmetic sequence are 30, 33,

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 3037 [0], given: 394

The first three terms in an arithmetic sequence are 30, 33, [#permalink]  30 Jul 2018, 09:59
Expert's post
00:00

Question Stats:

77% (00:38) correct 22% (00:44) wrong based on 31 sessions
The first three terms in an arithmetic sequence are 30, 33, and 36. What is the 80th term?

[Reveal] Spoiler: OA
267

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Sandy
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Manager
Joined: 27 Feb 2017
Posts: 188
Followers: 1

Kudos [?]: 78 [1] , given: 15

Re: The first three terms in an arithmetic sequence are 30, 33, [#permalink]  05 Aug 2018, 17:12
1
KUDOS
nth term=a1+(n-1)d=30+(80-1)*3=267
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 [0], given: 394

Re: The first three terms in an arithmetic sequence are 30, 33, [#permalink]  11 Aug 2018, 16:45
Expert's post
Explanation

While the sequence is clear (30, 33, 36, 39, 42, etc.), don’t spend time counting to the 80th term. Instead, find a pattern. Each new term in the list adds 3 to the previous term, so determine how many times 3 needs to be added. (By the way, the term “arithmetic sequence” means a sequence in which the same number is added or subtracted for each new term.)

Start with the first term, 30. To get from the first term to the second term, start with 30 and add 3 once. To get from the first term to the third term, start with 30 and add 3 twice. In other words, for the third term, add one fewer instance of 3: twice rather than three times.

To write this mathematically, say: 30 + 3(n-1), where n is the number of the term. (Note: it’s not necessary to write this out, as long as you understand the pattern.)

$$30 + (79 \times 3) = 267$$
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Sandy
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Re: The first three terms in an arithmetic sequence are 30, 33,   [#permalink] 11 Aug 2018, 16:45
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