Advertisements
Advertisements
Question
If a1 = 1, a2 = 1 and an = 2an−1 + an−2, n ≥ 3, n ∈ N, then find the first six terms of the sequence
Solution
a1 = 1, a2 = 1, an = 2an−1 + an−2
a3 = 2a(3−1) + a(3−2)
= 2a2 + a1
= 2 × 1 + 1 = 3
a4 = 2a(4−1) + a(4−2)
= 2a3 + a2
= 2 × 3 + 1 = 7
a5 = 2a(5−1) + a(5−2)
= 2a4 + a3
= 2 × 7 + 3 = 17
a6 = 2a(6−1) + a(6−2)
= 2a5 + a4
= 2 × 17 + 7
= 34 + 7
= 41
∴ The first six terms of the sequence are 1, 1, 3, 7, 17, 41 .......
APPEARS IN
RELATED QUESTIONS
Find the next three terms of the following sequence
`1/4, 2/9, 3/16, ...`
Find the first four terms of the sequence whose nth terms are given by an = n3 – 2
Find the first four terms of the sequence whose nth terms are given by an = (–1)n+1 n(n + 1)
Find the first four terms of the sequences whose nth terms are given by an = 2n2 – 6
Find the nth term of the following sequence
2, 5, 10, 17, ...
Find the nth term of the following sequence
3, 8, 13, 18, ...
Find the indicated terms of the sequences whose nth terms are given by
an = `(5"n")/("n" + 2)`; a6 and a13
Find the indicated terms of the sequences whose nth terms are given by
an = – (n2 – 4); a4 and a11
Find a8 and a15 whose nth term is an = `{{:(("n"^2 - 1)/("n" + 3)";", "n is even""," "n ∈ N"),(("n"^2)/(2"n" + 1)";", "n is odd""," "n ∈ N"):}`
Given F1 = 1, F2 = 3 and Fn = Fn–1 + Fn–2 then F5 is
