b Check if there is a common difference between consecutive terms.
A
a Yes
B
b No
Practice makes perfect
a The difference between the consecutive terms of an arithmetic sequence is constant. This means that if there is a common difference between the consecutive terms of the sequence, then the sequence is arithmetic. Let's find the difference between the first and second terms.
Let's do the same thing for the rest of the terms.
a_2-a_1
3x+6-(x+6)= 2x
a_3-a_2
5x+6-(3x+6)= 2x
a_3-a_2
7x+6-(5x+6)= 2x
In each case, the difference is constant and equal to 2x. This means that we have a common difference and therefore the given sequence is arithmetic.
b As in Part A, recall that the difference between the consecutive terms of an arithmetic sequence is constant. Let's calculate the difference between the consecutive terms of the given sequence.
a_2-a_1
3x+1-(x+1)= 2x
a_3-a_2
9x+1-(3x+1)= 6x
a_3-a_2
27x+1-(9x+1)= 18x
Unlike in Part A, the difference between consecutive terms is not constant. This means that the given sequence is not arithmetic.
