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0, 2, 2, 0, 2 The first five terms of a sequence are shown above. Aft
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27 Mar 2023, 01:27
27 Mar 2023, 01:27
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0, 2, 2, 0, –2
The first five terms of a sequence are shown above. After the second term, each term can be obtained by subtracting from the previous term the term before the previous term. What is the sum of the first 69 terms?
– 4
– 2
0
2
4
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The first five terms of a sequence are shown above. After the second term, each term can be obtained by subtracting from the previous term the term before the previous term. What is the sum of the first 69 terms?
– 4
– 2
0
2
4
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SEQUENCES
Re: 0, 2, 2, 0, 2 The first five terms of a sequence are shown above. Aft
[#permalink]
01 May 2023, 12:38
01 May 2023, 12:38
1
Expert Reply
OE
Given, every new term after the second term is obtained by subtracting from
the previous term the term before it.
According to which 𝑡3 = 𝑡2 − 𝑡1,𝑡4 = 𝑡3 − 𝑡2,𝑡5 = 𝑡4 − 𝑡3 𝑎𝑛𝑑 𝑠𝑜 𝑜𝑛..
So, the sequence goes as:
0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2,
…..
Here the sequence repeats for every set of six.
When 69 divided by 6 remainder is 3.
In, Dividend = Divisor × Quotient + Remainder format
→ 69 = 6 × 11 + 3
Therefore,
The sum of first 69 terms = 11 Sets (6 Terms) + 3 Terms.
We can observe the sum of each set is zero (0 + 2 + 2 + 0 + [−2] + [−2] = 0).
0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2,…….
So, the sum of 11 Sets (66 Terms) will be zero.
Therefore, the sum of 69 terms depends only on the last three terms (67th, 68th and
69th term) which will be 0 + 2 + 2 = 4.
Given, every new term after the second term is obtained by subtracting from
the previous term the term before it.
According to which 𝑡3 = 𝑡2 − 𝑡1,𝑡4 = 𝑡3 − 𝑡2,𝑡5 = 𝑡4 − 𝑡3 𝑎𝑛𝑑 𝑠𝑜 𝑜𝑛..
So, the sequence goes as:
0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2,
…..
Here the sequence repeats for every set of six.
When 69 divided by 6 remainder is 3.
In, Dividend = Divisor × Quotient + Remainder format
→ 69 = 6 × 11 + 3
Therefore,
The sum of first 69 terms = 11 Sets (6 Terms) + 3 Terms.
We can observe the sum of each set is zero (0 + 2 + 2 + 0 + [−2] + [−2] = 0).
0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2, −2, 0, 2, 2, 0, −2 −2, 0, 2, 2, 0, −2 −2,…….
So, the sum of 11 Sets (66 Terms) will be zero.
Therefore, the sum of 69 terms depends only on the last three terms (67th, 68th and
69th term) which will be 0 + 2 + 2 = 4.
gmatclubot
Re: 0, 2, 2, 0, 2 The first five terms of a sequence are shown above. Aft [#permalink]
01 May 2023, 12:38
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