A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an = an − 1 + an − 2 and a1 = 8, a2 = 6
a1
=
a2
=
a3
=
a4
=
a5
=
a3 = a3-1 + a3-2 = a2 + a1 = 6 + 8 = 14
a4 = a4-1 + a4-2 = a3 + a2 = 14 + 6 = 20
a5 = a5-1 + a5-2 = a4 + a3 = 20 + 14 = 34
The first five terms of the sequence are:
a1 = 8
a2 = 6
a3 = 14
a4 = 20
a5 = 34
To find the first five terms of the sequence defined by the given formulas, we can use the recursive formula.
Given: an = an-1 + an-2 and a1 = 8, a2 = 6
Let's calculate the first five terms step by step:
a1 = 8
a2 = 6
a3 = a2 + a1 = 6 + 8 = 14
a4 = a3 + a2 = 14 + 6 = 20
a5 = a4 + a3 = 20 + 14 = 34
Therefore, the first five terms of the sequence are:
a1 = 8
a2 = 6
a3 = 14
a4 = 20
a5 = 34