Question

Find the missing values.
$13,16,22,33,51,?$
A. $89$
B. $78$
C. $102$
D. $69$
E. None of these

Answer 1

Hint: Find the difference between the given numbers until we get the same difference. And, then add the last number to the previously last number respectively. Finally, we will get the answer and find the correct option for this question.

Complete step-by-step answer:
Here given question is,
$ \Rightarrow $$13,16,22,33,51,?$
Find the difference between the all numbers, we get
$ \Rightarrow $$3,6,11,18$------$I$
Here the difference is not the same. Again, we will find the different
$ \Rightarrow $\[3,5,7\]---------$II$
Here different is not same again we will find the difference between all numbers we get
$ \Rightarrow $\[2,2\] ----------$III$
Here different will be same so we will add $2$ on above equation $II$ we will get
$3,5,7,9$
We will add $9$ on equation $I$ we will get
$ \Rightarrow $$3,6,11,18,27$
We will add $27$ on question we will get answer
$ \Rightarrow $$13,16,22,33,51,78$

Here answer will be option B answer $78$.

Additional information:
A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence. Here it will be under the sequence of numbers. A geometric sequence is one in which a term of a sequence is obtained by multiplying the previous term by a constant.

Note: We will concentrate on what is the difference of a sequence. Here we will find the answer when it comes in Same order as in the question. This time we will add the number and find the answer. We will know how to form the sequence in question then only we will find the answer. We will use different types of methods in different questions.