Question

Ankit, a cunning math wizard has a nasty habit of cheating people with numbers. He tells Ricky, " I will give you some sums which are obtained by adding some numbers. If you can tell me the logic behind it, I will pay you the amount in rupees equal to the sum of all the numbers. But if you fail, you will have to pay me twice the number amount." The sums given by Ankit are 3,17,49,105,191,...1281,1673. Ricky tries his level best to find the logic but fails to do so. As a result, how much does Ankit manage to extract from Ricky?

Answer 1

Answer:

Rs.11,506

Step-by-step explanation:

The series is 3,17,49,105,191,...1281,1673

By careful observation you will find the nth term follows this pattern

T(n) = n³ + 3n² - 2n + 1 where n = 1, 2, 3, …

Now sum of the series can be written as

S(n) = [n²(n + 1)²]/4 + 3[n(n + 1)(2n + 1)]/6 - 2[n(n + 1)]/2 + n

Here 1673 is the 11th term, so when we substitute 11 for n, we get the answer, which is

S(11) = [11² x 12²]/4 + [3 x 11 x 12 x 23]/6 - 2[11 x 12]/2 + 11

=> S(11) = [121 x 36] + [66 x 23] - 132 + 11

=> S(11) = 4356 + 1518 - 121

=> S(11) = 5753

Since Ricky could not answer, he will have to pay twice the amount.

Thus the sum extracted by Ankit is Rs. 2 * 5753 =    Rs.11,506