If a0 2 and a1 3 and an 2ani an2 find a2 a3 and a4Soluti

If a_0 = 2, and a_1 = 3, and a_n = 2a_n_i - a_n_2, find a_2, a_3, and a_4.

Solution

Solution:

given

a₀ =2 a₁ =3

a_n =2a_n-1 - a_{n-2 --------------------------(1)}

put n=2 to get a₂

a_{2 =} 2a_2-1 - a_2-2

₌2a₁ -a₀

=2(3)-2

=6-2

a₂ =4 -----------------(2)

Put a=3 in (1)

a₃ =2a_3-1 - a_3-2

a₃=2a₂ -a₁

Sub a₂ from(2) we get

a₃=2(4)-3

=8-3

a₃=5 ----------------------------(3)

Put n=4

a₄ =2a_4-1 -a_4-2

=2a₃ -a₂

substitute   a_{3 from} (3)

=2(5)-4

=10-4

a₄ =6