Question

What is the next number in the sequence 21, 34, 55, 89, 144?
A.169
B.213
C.223
D.233

Answer 1

Hint: In this question, we need to determine the next term of the series 21, 34, 55, 89, 144 such that the values given in the preceding terms satisfies. For this, we will establish a relation between the given terms and evaluate the values of the succeeding terms.

Complete step-by-step answer:
Let the next term of the sequence be ‘x’. Then, the sequence will be 21, 34, 55, 89, 144, x.
After careful observation on the terms in the sequence we can see that each succeeding term is the sum of the two preceding terms such that
The third term in the sequence is 55 which is the sum of the two preceding terms 34 and 21 so, we can write $55=34+21$ .
Similarly, the fourth term in the sequence is 89 which is the summation of the two preceding terms 55 and 34 so, we can write $89=55+34$ .
Again, the fifth term in the sequence is 144 which is the summation of the two preceding terms 89 and 55 so, we can write $144=89+55$ .
As the same condition is satisfying to all the terms in the sequence so, we can apply the same condition to evaluate the next term of the sequence 21, 34, 55, 89, 144, x.
So, ‘x’ will be the summation of the two preceding terms 144 and 89. Therefore, $x=144+89=233$.
Hence, the value of the next term in the sequence $21$ , $34$ , $55$ , $89$ , $144$ is $233$ .

Note: In this type of questions, students need to establish a condition which satisfies all the mathematical representations. However, it is not always essential that a fixed mathematical condition is there to solve this type of questions, it varies from person perspective.