Question

How do you tell whether the sequence $ 3,5.5,8,10.5,13 $ is arithmetic?

Answer 1

Hint: As we know that an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. We know the formula of the sum of arithmetic sequence is $ {S_n} = \dfrac{n}{2}\{ 2a + (n - 1)d\} $ where $ n $ is the number of terms, $ a = $ first term and $ d $ is the common difference. To check any sequence if it is arithmetic or not, we can take any number and then subtract it by the previous one and if the result is always the same or constant, then we can say that the sequence is arithmetic.

Complete step-by-step answer:
As the per given question we have the sequence: $ 3,5.5,8.10.5,13 $ . To check this is arithmetic or not, we will take the number and subtract it by the previous one.
In the first case: $ 5.5 - 3 = 2.5 $ .
In the second case $ 8 - 5.5 = 2.5 $
In the third case $ 10.5 - 8 = 2.5 $ and so on.
We can see that there is a common difference in the terms, i.e. constant, so the sequence is arithmetic.
Hence we can say that the sequence $ 3,5.5,8,10.5,13 $ is an arithmetic sequence.

Note: We should be aware of the arithmetic sequence and their formula before solving this kind of question. We should carefully substitute the values and solve them. Also we can find the sum of the given arithmetic sequence by adding the first and last term and then divide the sum by two, this is also a formula when the first and the last term is given in the question. And then the sum of the sequence will be the number of terms multiplied by the average number of terms in the sequence. The formula can be written as $ S = \dfrac{n}{2}(a + l) $ where the number of terms and $ a,l $ are first and last terms.