Final answer:
To determine if a sequence is arithmetic, we check if the difference between consecutive terms is the same. Sequences a) and b) are arithmetic sequences.
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant.
The given sequences are:
a) 10, 14, 18, 22, 26
b) 14, 18, 22, 26, 30
c) 10, 15, 20, 25, 30
d) 4, 8, 12, 16, 20
To determine if a sequence is arithmetic, we check if the difference between consecutive terms is the same. Let's calculate the differences for each sequence:
a) Difference = 14 - 10 = 4; 18 - 14 = 4; 22 - 18 = 4; 26 - 22 = 4. The difference is 4, so sequence a) is arithmetic.
b) Difference = 18 - 14 = 4; 22 - 18 = 4; 26 - 22 = 4; 30 - 26 = 4. The difference is 4, so sequence b) is arithmetic.
c) Difference = 15 - 10 = 5; 20 - 15 = 5; 25 - 20 = 5; 30 - 25 = 5. The difference is 5, so sequence c) is not arithmetic.
d) Difference = 8 - 4 = 4; 12 - 8 = 4; 16 - 12 = 4; 20 - 16 = 4. The difference is 4, so sequence d) is arithmetic.
Therefore, the arithmetic sequences are a) 10, 14, 18, 22, 26 and b) 14, 18, 22, 26, 30.