Question

problems 7 - 9: given the first term and rule:
circle if it is an arithmetic sequence, geometric sequence or neither
write the first 4 terms of each sequence.

1. first term 1

rule multiply the previous term by 1

1. first term 1

rule add 1 to the previous number and square it

1. first term 12

rule add 4 to the previous number
arithmetic sequence
geometric sequence
neither

Explanation:

Step1: Analyze problem 7

First - term \(a_1 = 1\), rule \(a_{n}=a_{n - 1}\times1\). First 4 terms: \(1,1,1,1\). It's geometric (common - ratio 1).

Step2: Analyze problem 8

First - term \(a_1 = 1\), rule \(a_{n}=(a_{n - 1}+1)^2\). Terms: \(1,4,25,676\). Neither.

Step3: Analyze problem 9

First - term \(a_1 = 12\), rule \(a_{n}=a_{n - 1}+4\). Terms: \(12,16,20,24\). Arithmetic.

Answer:

1. Geometric Sequence, 1, 1, 1, 1
2. Neither, 1, 4, 25, 676
3. Arithmetic Sequence, 12, 16, 20, 24