Question

Write the first five terms of the following sequence and obtain the corresponding series: 

`a_1 = a_2 = 2, a_n = a_(n-1) -1, n > 2`

Answer 1

a₁ = a₂ = 2.... (given)

and a_n = a_n−1 −1, n > 2

Putting n = 3, 4, 5,

a₃ = a₂ − 1 = 2 − 1 = 1

a₄ = a₃ − 1 = 1 − 1 = 0

a₅ = a₄ − 1 = 0 − 1 = −1

Hence, the five terms of the sequence are 2, 2, 1, 0 and −1.

Corresponding series = 2 + 2 + 1 + 0 + (−1)