Question

What is the next item in this pattern: 100, 81, 64, 49, ………. ?

Answer 1

Hint: Here in this question we have been asked to find the next item in the given list of pattern 100, 81, 64, 49, ………. Here if we observe the given pattern carefully it can be simply written as ${{10}^{2}},{{9}^{2}},{{8}^{2}},{{7}^{2}},........$

Complete step-by-step solution:
Now considering from the question we have been asked to find the next item in the given list of pattern 100, 81, 64, 49, ……….
When we observe the given pattern carefully it can be also represented as follows in a simple manner: ${{10}^{2}},{{9}^{2}},{{8}^{2}},{{7}^{2}},........$ .
So now we can say that the first term is square of 10 and the second term is the square of 9 that is 1 less 10 and the next term is given as the square of 8 that is one less 9 and the last given term is the square of 7 that is one less than 8 and so on.
As we have been asked, for the next term of the given pattern this will be given by the square of one less than 7 that is 6.
Hence we can conclude that the next item in the given list of pattern 100, 81, 64, 49, ………. will be ${{6}^{2}}=36$.

Note: While answering questions of this type we should carefully observe the pattern and the last term. Someone can assume that the last term is 36 and answer the question as 25 due to some overlook which will be a wrong conclusion.