Question

11, 13, 23, 36, 81, 146, ? ​

Answer 1

11, 13, 23, 36, 81, 146,

(next term is obtained by adding squares of digits of the previous term with itself.)

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Answer 2

The next term of the series is 199.

• A series in mathematics is essentially a description of the process of successively adding an infinite number of quantities to a specified initial quantity. A significant component of calculus and its generalisation, mathematical analysis, is the study of series.
• Most branches of mathematics use series, including combinatorics, where generating functions are used to explore finite structures. In addition to being widely utilised in mathematics, infinite series are also used extensively in physics, computer science, statistics, and finance, among other quantitative fields.

Here, according to the given information, we are given that,

11, 13, 23, 36, 81, 146, ? ​

The first term is 11.

Now, adding the sum of the square of the digits of 11 with 11, we get,

$11+1^{2} +1^{2} = 13,$ which is the second term of the given series.

Again, similarly, $13+1^{2} +3^{2} = 23.$

Similarly, $23+2^{2} +3^{2} = 36.$

Proceeding in a similar manner, we get, $146+1^{2} +4^{2} +6^{2} = 199.$

Hence, the next term of the series is 199.

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