Question

Write the first five terms of each sequence. Determine whether each sequence is

arithmetic, geometric, or neither
1.a(1) Ba(n) = a(n-1) 3 forn > 2.
2.6(1) = 1,6(n) = 3.b(n - 1) for n 2.
3.c(1) = 3,c(n) = -cn-1) + 1 forn 22.
4.d(1) = 5,d(n) = din - 1) + n for n 2 2

Answer 1

The first five terms of the sequences and their types are as follows: Sequence 1.a: 1, 3, 9, 27, 81 (geometric), Sequence 2.b: 1, 3, 9, 27, 81 (geometric), Sequence 3.c: 3, -10, 31, -94, 283 (neither), Sequence 4.d: 5, 7, 12, 20, 35 (neither).

Step-by-step explanation:

Sequence 1.a: The first five terms of the sequence are 1, 3, 9, 27, and 81. This sequence is a geometric sequence with a common ratio of 3, as each term is obtained by multiplying the previous term by 3.

Sequence 2.b: The first five terms of the sequence are 1, 3, 9, 27, and 81. This sequence is also a geometric sequence with a common ratio of 3, as each term is obtained by multiplying the previous term by 3.

Sequence 3.c: The first five terms of the sequence are 3, -10, 31, -94, and 283. This sequence is neither arithmetic nor geometric, as there is no constant difference or ratio between terms.

Sequence 4.d: The first five terms of the sequence are 5, 7, 12, 20, and 35. This sequence is neither arithmetic nor geometric, as there is no constant difference or ratio between terms.