Write the first five terms of the sequence and obtain the corresp… - Vidyadip

Question

Write the first five terms of the sequence and obtain the corresponding series a₁ = a₂ = 2, a_n = a_n-1 - 1, n > 2.

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Answer

Given: a₁ = a₂ = 2, a_n = a_n-1 - 1, n > 2
Putting n = 3, 4 and 5, we get
a₃ = a_3-1 - 1 = a₂ _{- 1} = 2 - 1 = 1
a₄ = a_4-1 - 1 = a₃ _{- 1} = 1 - 1 = 0
a₅ = a_5-1 - 1 = a₄ _{- 1} = 0 - 1 = -1
Hence the first five terms are 2, 2, 1, 0, -1.
Therefore, corresponding series is 2 + 2 + 1 + 0 + (-1) + .......

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