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.