Question

What value would replace the question mark in \[100,121,144,?,196,225\]
A). \[149\]
B). \[179\]
C). \[189\]
D). \[169\]

Answer 1

Hint: First we have to know that in mathematics, a sequence is a list of elements (or objects) which have been ordered in a sequential way such that each element either comes before, or after, every other element.
To find the missing number in the given sequence, we need to find the logic of how the numbers are arranged in the given sequence. Using that logic we find the missing number in the given sequence.

Complete step-by-step solution:
Given \[100,121,144,?,196,225\]--(1)
Since \[100\] is the square of \[10\] i.e., \[{10^2} = 100\].
Similarly, \[121\] is the square of \[11\] , \[144\] is the square of \[12\],\[196\] is the square of \[14\] and \[225\] is the square of \[15\].
Then the sequence (1) can also be written as follows
\[{10^2},{11^2},{12^2},?,{14^2},{15^2}\]-----(2)
In the sequence (2), elements are arranged sequential as squares of the natural numbers starting from \[10\]. Since the number comes after \[12\] is \[13\] in the natural number set. Hence the question mark will be replaced by \[{13^2} = 169\].
Hence the correct option is (D) \[169\].

Additional information: Logic involves both inductive (also called inductive reasoning) and deductive logic (also called deductive reasoning).
 Deductive logic is a detailed well-ordered process that aims to provide definite support for a possible conclusion. On the other hand, Inductive logic is the process by which a conclusion is arrived at by making limited observations. Inductive logic can show that a conclusion is probably true, but deductive logic can show that a conclusion must be true.

Note: A series is a sum of a sequence of terms. It means a series is a list of numbers with additional operations between them.
Logic is a tool used to develop reasonable conclusions (formal reasoning) based on given statements or propositions (set of data). Hence logic is a way to improve critical thinking skills to find a solution by studying the problem and implementing strategies not just looking at a problem.