Question

Question 13 Write the first five terms of the following sequence and obtain the corresponding series: a1=a2=2, an = a(n-1) - 1, n>2

Class X1 - Maths -Sequences and Series Page 181

Answer 1

We have ,
a₁ = a₂ = 2
and ,
$a_n=a_{n-1}-1$
Putting n = 3, then, a₃ = a₃₋₁ -1 = a₂ -1 = 2 - 1 = 1
putting n=4, then, a₄ = a₄₋₁ - 1 = a₃ -1 = 1 -1 = 0
Putting n = 5, then, a₅ = a₅₋₁ - 1 = a₄ -1 = 0 - 1 = -1
Putting n= 6, then, a₆ = a₆₋₁ -1 = a₅ -1 = -1 - 1 = -2
Hence, 2, 2, 1, 0, -1, are first five terms of given series.