Question

Is this an arithmetic sequence? How do you know? 24, 29, 34, 40

Answer 1

No, It isn’t... because if you add 5 to the first, you have a defined sequence at the second number, but if you add 5 to the third you get too many!

Answer 2

$\text{Consider the sequence, }24,\ 29,\ 34,\ 40\\ \\ \text{we know that a sequence is an arithmatic sequence if the difference}\\ \text{between two consecutive terms is equal.}\\ \text{that is the difference of succesive terms in an arithmatic sequence }\\ \text{is always equal.}\\ \\ \text{so in order to check whether the given sequence is an arithmatic sequence}\\ \text{we check the difference between the given terms. so}$

$29-24=5,\\ \\ 34-29=5,\\ \\ 40-34=6\\ \\ \text{here we can see that the difference between the last two terms is different}\\ \text{from the other two common differences.}$

Hence the given sequence is Not an arithmetic sequence.