The first five terms of each sequence can be written from the nth term of the sequence and the type of sequence are, arithmetic, geometric, geometric, geometric, and geometric respectively.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
The sequences are:
1. a(1) = 7, a(n) = a(n - 1) - 3 for n > 2.
Plug n = 2 in the a(n)
a(2) = a(2 - 1) - 3
a(2) = a(1) - 3
a(2) = 7 - 3
a(2) = 4
lug n = 3
a(3) = 1
The first five terms are:
7, 4, 1, -2, -5 (arithmetic sequence)
2. b(1) = 2, b(n) = 2[b(n - 1) - 1] for n > 2.
Similarly,
The first five terms are:
2, 2, 2, 2, 2 (geometric sequence)
3. c(1) = 3. c(n) = 10 • c(n - 1) for n > 2.
The first five terms are:
3, 30, 300, 3000, 30000 (geometric sequence)
4. d(1) = 1, d(n) = n • d(n - 1) for n > 2.
1, 2, 6, 24, 48 (geometric sequence)
Thus, the first five terms of each sequence can be written from the nth term of the sequence and the type of sequence are, arithmetic, geometric, geometric, geometric, and geometric respectively.
Learn more about the sequence here:
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