Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Combination of Sequence.

## Logic and combination of sequence (B.Stat Objective)

The two sequence of numbers {1,4,16,64,…..} and {3,12,48,192,…..} are mixed as follows {1,3,4,12,16,48,64,192,….}. One of the numbers in the mixed series is 1048576. Then the number immediately preceeding it is

- 262144
- 786432
- 814572
- 786516

**Key Concepts**

Logic

Sequence

Integers

## Check the Answer

But try the problem first…

Answer: 786432.

B.Stat Objective Question 79

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

The first series is of form \(4^{r}\) for \(r \geq 0\) \(r \in\) set of natural numbers the second series is of form \(3 \times 4^{r}\) for \(r \geq 0\) \(r \in\) set of natural numbers and the third series is of \(4^{r}\),\(3 \times 4^{r}\) in alternate element form for \(r \geq 0\) \(r \in\) set of natural numbers

Second Hint

given that 1048576=\(4^{r}\)=\(4^{10}\)

Final Step

then preceeding term \(3 \times 4^{9}\)=(3)(262144)=786432.

## Other useful links

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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