Question

Consider all numbers which can be represented by the sum of different powers of 5. For eg:- 1(5^0), 6(5^0 + 5^1), 26(5^2 + 5^0) etc.. If we arrange them in ascending order, what will be the number of 16276 (given that it is the sum of different powers of 5).

Answer 1

Given :- Consider all numbers which can be represented by the sum of different powers of 5. For eg:- 1(5^0), 6(5^0 + 5^1), 26(5^2 + 5^0) etc.. If we arrange them in ascending order, what will be the number of 16276 (given that it is the sum of different powers of 5).

Answer :-

→ first number = 1 = 5⁰

→ second number = 6 = 5⁰ + 5¹

→ Third number = 26 = 5⁰ + 5²

→ fourth number = 5⁰ + 5³ = 126

→ fifth number = 5⁰ + 5⁴ = 626

→ sixth number = 5⁰ + 5⁵ = 3126

→ seventh number = 5⁰ + 5⁶ = 15626

conclusion :-

• nth number = 5⁰ + 5^(n - 1) or 1 + 5^(n - 1) { Except for first number . }

then,

→ (16276)th number in ascending order = 5⁰ + 5^(16276 - 1) = (5⁰ + 5¹⁶²⁷⁵) or (1 + 5¹⁶²⁷⁵) .

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Answer 2

Step-by-step explanation:

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